EQ - 3

[Audio] Let us now investigate the earthquake engineering loading definition, structural analysis and design, with the commercial software ProtaStructure 2019 SP7. Two methods of structural analysis shall be conducted, firstly the equivalent static lateral force analysis method, and secondly the multi-modal response spectrum analysis method..

[Audio] First, the equivalent static lateral force analysis method, using a high-ductility inelastic analysis approach, shall be performed on a Shear and Core Wall (or Braced Frame) stabilized frame as Approach 1, and on a Moment Frame stabilized frame as Approach 2..

[Audio] In the equivalent static lateral force analysis method, horizontal earthquake loads are defined by selecting Analysis, then, Building Analysis, then, Pre-Analysis Tab, then, Storey Loads and Parameters to populate the table with earthquake loads EQX and EQY located at the coordinates of the centre of mass. And this is repeated for all storeys, based on the distribution assumed by the equivalent static lateral force analysis method..

[Audio] Next, the mass for period calculations is defined by selecting Analysis, then, Building Analysis, then, Pre-Analysis Tab, then, Parameters, then, Lateral Loading Tab, then, Insert Live Load Participation Factor as say 0.3, to define 30% of the live load as contributing to the mass that affects the structural natural periods in the dynamic excitation..

[Audio] The structural analysis is then performed firstly by decomposing slab loads onto beams by choosing Analysis, then, Load Decomposition by FE, then, Floor Mesh and Analysis Tab, then, Batch FE Chasedown. And secondly, we would run the overall 3D building analysis by choosing Analysis, then, Building Analysis, then, Analysis Tab, then, Building Analysis and Perform Eigenvalue Analysis, then, Start..

[Audio] For the first output, we could compute the fundamental modal periods in x and y, by selecting Analysis, then, Building Analysis, then, Post-Analysis Tab, then, Model and Analysis Results Display, then, Results Tab, then, Diagrams, then, Displacements for the chosen modal load cases to read the fundamental modal period in x as 0.53 seconds, and the fundamental modal period in y as 2.31 seconds, both similar to the reference assumptions..

[Audio] The fundamental modal periods in x and y could also be obtained by selecting Analysis, then, Building Analysis, then, Reports Tab, then, Eigenvalue Results Report to read the fundamental modal period in x as 0.53 seconds at 73% modal participating effective mass, and the fundamental modal period in y as 2.31 seconds at 87% modal participating effective mass, both similar to the reference assumptions..

[Audio] Next, we could compute the seismic base moment in x from EQX by summing the effects of the axial force push-pull moment in x, and the wall bending moment in x.. The axial force push-pull moment in x is obtained by choosing Analysis, then, Building Analysis, then, Post-Analysis Tab, then, Model and Analysis Results Display, then, Results Tab, then, Diagrams, then, N to read the axial forces at the bottom of the column for the chosen load case EQX, which could then be multiplied by its lever arm of 30m, and summed to yield 383,280 kilo Newton meter push-pull moment..

[Audio] The wall bending moment in x is obtained by choosing Graphics, then, Right-Click Wall, then, RC Column/Wall Design to read the wall bending moment at the bottom of the wall for the chosen load case EQX, which could then be summed to yield 337,724 kilo Newton meter bending moment. The summation of the effects of the axial force push-pull moment in x, and the wall bending moment in x, is then computed as 721,004 kilo Newton meter bending moment, which tallies well with the seismic base moment input of 722,000 kilo Newton meter..

[Audio] Next, we could compute the seismic base shear in x from EQX by summing the effects of the wall shear in x, and the column shear in x.. The wall shear in x is obtained by choosing Graphics, then, Right-Click Wall, then, RC Column/Wall Design to read the wall shear force at the bottom of the wall for the chosen load case EQX, which could then be summed to yield 33,304kN shear force..

[Audio] The column shear in x is obtained by choosing Analysis, then, Building Analysis, then, Post-Analysis Tab, then, Model and Analysis Results Display, then, Results Tab, then, Diagrams, then, V2 to read the shear forces at the bottom of the column for the chosen load case EQX, which could then be summed to yield 1,100kN shear. The summation of the effects of the wall shear in x, and the column shear in x, is then computed as 34,404kN shear force, which tallies well with the seismic base shear input of 34,400kN..

[Audio] The lateral deflection in x is obtained by choosing Analysis, then, Building Analysis, then, Post-Analysis Tab, then, Model and Analysis Results Display, then, Displacements, then, x to read the 28mm inelastic deflection at the top of the building for the chosen load case EQX. Thus, the elastic deflection is obtained by multiplying the displacement compatibility factor Cd of 3.85 to the inelastic deflection, to yield 108mm..

[Audio] Next, we could compute the seismic base moment in y from EQY by summing the effects of the axial force push-pull moment in y.. The axial force push-pull moment in y is obtained by choosing Analysis, then, Building Analysis, then, Post-Analysis Tab, then, Model and Analysis Results Display, then, Results Tab, then, Diagrams, then, N to read the axial forces at the bottom of the column for the chosen load case EQY, which could then be multiplied by its lever arm of 30m, and summed to yield 216,840 kilo Newton meter push-pull moment, which tallies fairly well with the seismic base moment input of 210,000 kilo Newton meter..

[Audio] Next, we could compute the seismic base shear in y from EQY by summing the effects of the column shear in y, and the wall shear in y.. The column shear in y is obtained by choosing Analysis, then, Building Analysis, then, Post-Analysis Tab, then, Model and Analysis Results Display, then, Results Tab, then, Diagrams, then, V3 to read the shear forces at the bottom of the column for the chosen load case EQY, which could then be summed to yield 8,392kN shear..

[Audio] The wall shear in y is obtained by choosing Graphics, then, Right-Click Wall, then, RC Column/Wall Design to read the wall shear force at the bottom of the wall for the chosen load case EQY, which could then be summed to yield 1,616kN shear force. The summation of the effects of the column shear in y, and the wall shear in y, is then computed as 10,008kN shear force, which tallies well with the seismic base shear input of 10,000kN..

[Audio] The lateral deflection in y is obtained by choosing Analysis, then, Building Analysis, then, Post-Analysis Tab, then, Model and Analysis Results Display, then, Displacements, then, y to read the 132mm inelastic deflection at the top of the building for the chosen load case EQY. Thus, the elastic deflection is obtained by multiplying the displacement compatibility factor Cd of 3.85 to the inelastic deflection, to yield 508mm..

[Audio] Next, the second method of structural analysis shall be conducted, i.e. the multi-modal response spectrum analysis method, using a high-ductility inelastic analysis approach, on a Shear and Core Wall (or Braced Frame) stabilized frame as Approach 1, and on a Moment Frame stabilized frame as Approach 2..

[Audio] In the multi-modal response spectrum analysis method, the code defining the response spectrum is chosen by selecting Analysis, then, Building Analysis, then, Pre-Analysis Tab, then, Parameters, then, select the Earthquake Code..

[Audio] Subsequently, the response spectrum is defined by selecting Analysis, then, Building Analysis, then, Pre-Analysis Tab, then, Seismic Parameters, then, choosing the seismic parameters of peak ground acceleration PGA of 40%g, importance factor of 1.00, soil response parameter or seismic coefficient of 1.10 and 1.60, behaviour factor or response modification factor of 5.50 (and thus defining the design spectrum), overstrength factor of 2.80 (however inserting 1.0 in this software so that the effects are not automatically altered, instead manually assessed subsequently), and displacement compatibility factor of 3.85 (not inserted herewith, manually assessed subsequently), choosing say 12 dynamic modes to participate in the multi-modal response analysis. Manually amend spectral amplitudes where required, such as to define a high period spectral acceleration plateau. Note that the design inelastic spectrum cannot be defined by scaling the elastic spectrum by the response modification factor in the load case, or the load combination case, because the former may have a minimum high period, spectral acceleration plateau. Ensure that the default 5% of critical viscous damping is chosen so that no further scaling of the elastic response spectrum is inadvertently performed..

[Audio] Consequently, the earthquake load cases within the loading combinations are defined by selecting Analysis, then, Building Analysis, then, Pre-Analysis Tab, then, Loading Combinations, then, Load Cases, then, Edit EQX and EQY, then, selecting Earthquake Spectrum Loading..

[Audio] Next, the mass for period calculations is defined by selecting Building Setout, then, Edit Storey, then, Insert Live Load Participation Factor as say 0.3 for each storey, to define 30% of the live load as contributing to the mass that affects, firstly, the structural natural periods, and secondly, the dynamic weight, in the dynamic excitation..

[Audio] Next, the element stiffness modifiers need to be respecified, as the selection of multi-modal response spectrum analysis, inadvertently resets the modifiers to some other defaults. To redefine element stiffness modifiers, select Analysis, then, Building Analysis, then, Model Options, then, Model Tab, then, Material and Section Effective Stiffness Factor, then, Reset Beam Bending Stiffness to 0.70 say (note to utilise elastic modulus modifier as the bending stiffness modifier does not work in ProtaStructure 2019 SP7.0) and the remaining stiffnesses to 1.0..

[Audio] The structural analysis is then performed firstly by decomposing slab loads onto beams by choosing Analysis, then, Load Decomposition by FE, then, Floor Mesh and Analysis Tab, then, Batch FE Chasedown. And secondly, we would run the overall 3D building analysis, modal eigenvalue analysis, and response spectrum analysis, by choosing Analysis, then, Building Analysis, then, Analysis Tab, then, Building Analysis and Perform Eigenvalue Analysis, then, Start..

[Audio] The fundamental modal periods in x and y are then obtained by selecting Analysis, then, Building Analysis, then, Reports Tab, then, Eigenvalue Results Report to read the fundamental modal period in x as 0.55 seconds at 73% modal participating effective mass, and the fundamental modal period in y as 2.35 seconds at 87% modal participating effective mass, both similar to the reference assumptions. With the adopted say 12 dynamic modes, a cumulative participating mass percentage of 90% in x direction, and 99% in y direction is obtained, more than the usually acceptable threshold of 90%..

[Audio] All the effects computed before for the Equivalent Static Lateral Force Analysis Method, namely the base moment, base shear, and elastic deflections from EQX and EQY, as well as the summation of modal forces at each diaphragm within the Storey Parameters and Loads, can now be recalculated here for the Multi-Modal Response Spectrum Analysis Method, using the same procedures adopted in the previous section. For low rise or regular buildings, the magnitudes of the base moment and base shear effects, are generally lesser in the Multi-Modal Response Spectrum Analysis Method, compared to the Equivalent Static Lateral Force Analysis Method, because the modal effective mass of the dominant fundamental mode is only a proportion of the full dynamic mass, and higher modes, although subject to higher spectral accelerations, have lower participations. For high rise or irregular buildings, the magnitudes of the base moment and base shear effects, have the potential to be higher in the Multi-Modal Response Spectrum Analysis Method, compared to the Equivalent Static Lateral Force Analysis Method, because higher modes, although have lower participations, are still significant nevertheless, and are also subject to higher spectral accelerations..

[Audio] Let us now investigate the earthquake engineering loading definition, structural analysis and design, with the commercial software OASYS GSA 8.7.0.31. Three methods of structural analysis shall be conducted, firstly the equivalent static lateral force analysis method, secondly the multi-modal response spectrum analysis method, and thirdly the time history response analysis method..

[Audio] First, the equivalent static lateral force analysis method, using a high-ductility inelastic analysis approach, shall be performed on a Shear and Core Wall (or Braced Frame) stabilized frame as Approach 1, and on a Moment Frame stabilized frame as Approach 2..

[Audio] CSC Orion R18 SP5, ProtaStructure 2018 SP4.0, or ProtaStructure 2019 SP7.0 are good geometrical modelling tools, and as such models could be best created in these software before converting the structural analytical model into OASYS/GSA. This conversion could be done just by applying the Maverick Excel Convertor on the generated SAP2000 v15 text file from CSC Orion R18 SP5, ProtaStructure 2018 SP4.0, or ProtaStructure 2019 SP7.0. In this conversion, all finite elements geometries, sections properties, section modifiers, materials, applied loads, and boundary conditions would be converted. Step 4 is essentially a quality assurance check to ensure that the CSC Orion or ProtaStructure and OASYS/GSA models are consistent in terms of total dead and live load at each storey..

[Audio] Thus here are the illustrated steps to convert the generated SAP2000 v15 text file from CSC Orion R18 SP5, ProtaStructure 2018 SP4.0, or ProtaStructure 2019 SP7.0 through the Maverick Excel Convertor to a GSA text file..

[Audio] This GSA text file could then be imported in GSA through the command, File, then, Import, then, Text (GWA file)..

[Audio] In the equivalent static lateral force analysis method, to check the magnitude and direction of the defined and assigned EQX, we would choose Diagram Settings, then, Loading, then, Nodal Loading, then, Node Loads, Force to display a vector diagram showing unique nodal loads in varying magnitudes and directions. In doing so, we would need to choose to display the appropriate load case EQ x.. Note that any force could be selected for annotation by selecting the Select for Annotation command button, and subsequently selecting the node..

[Audio] In the equivalent static lateral force analysis method, to check the magnitude and direction of the defined and assigned EQY, we would choose Diagram Settings, then, Loading, then, Nodal Loading, then, Node Loads, Force to display a vector diagram showing unique nodal loads in varying magnitudes and directions. In doing so, we would need to choose to display the appropriate load case EQ y.. Note that any force could be selected for annotation by selecting the Select for Annotation command button, and subsequently selecting the node..

[Audio] Next, the mass for period calculations is defined by selecting Analysis, then, New Analysis Task, then, Modal Dynamic, then, Insert Mass Derived from Loads as say G + 0.3Q, to define 30% of the live load as contributing to the mass that affects the structural natural periods in the dynamic excitation. Even if vertical modes and response are not being assessed, in either the multi-modal response spectrum analysis method, or the time history response analysis method, there is no option in the software to not include mass only for vertical modes. The option to add additional vertical restraint should thus not be used as it affects modes in all directions..

[Audio] To perform the overall 3D building analysis, we would choose Analysis, then, Analyse All..

[Audio] For the first output, we could compute the fundamental modal periods in x and y, by selecting Contour Settings, then, Beam and Spring Element Results, then, Beam and Spring Displacements, then, Resolved Element Translation Absolute U to read the fundamental modal period in x as 0.55 seconds, and the fundamental modal period in y as 2.35 seconds, both similar to the reference assumptions..

[Audio] The fundamental modal periods in x and y could also be obtained by selecting Output, then, Global Results, then, Dynamic Summary, then, OK to read the fundamental modal period in x as 0.55 seconds at 71% modal participating effective mass, and the fundamental modal period in y as 2.35 seconds at 87% modal participating effective mass, both similar to the reference assumptions..

[Audio] Next, we could compute the seismic base moment in x from EQX by summing the effects of the axial force push-pull moment in x, and the wall bending moment in x.. The axial force push-pull moment in x is obtained by choosing Contour Settings and/or Diagram Settings, then, Beam and Spring Element Results, then, Beam and Spring Forces and Moments, then, Axial Force, Fx to read the axial forces at the bottom of the column for the chosen load case EQX, which could then be multiplied by its lever arm of 30m, and summed to yield 384,720 kilo Newton meter push-pull moment..

[Audio] The wall bending moment in x is obtained by choosing Contour Settings and/or Diagram Settings, then, Assembly Results, then, Assembly Forces and Moments, then, Assembly Moment, Mzz to read the bending moment at the bottom of the wall for the chosen load case EQX, which could then be summed to yield 323,044 kilo Newton meter bending moment. The summation of the effects of the axial force push-pull moment in x, and the wall bending moment in x, is then computed as 707,764 kilo Newton meter bending moment, which tallies fairly well with the seismic base moment input of 722,000 kilo Newton meter..

[Audio] Next, we could compute the seismic base shear in x from EQX by summing the effects of the wall shear in x, and the column shear in x.. The wall shear in x is obtained by choosing Contour Settings and/or Diagram Settings, then, Assembly Results, then, Assembly Forces and Moments, then, Assembly Force, Fy to read the wall shear force at the bottom of the wall for the chosen load case EQX, which could then be summed to yield 33,060kN shear force..

[Audio] The column shear in x is obtained by choosing Contour Settings and/or Diagram Settings, then, Beam and Spring Element Results, then, Beam and Spring Forces and Moments, then, Shear Force, Fz to read the shear forces at the bottom of the column for the chosen load case EQX, which could then be summed to yield 1,156kN shear. The summation of the effects of the wall shear in x, and the column shear in x, is then computed as 34,216kN shear force, which tallies well with the seismic base shear input of 34,400kN..

[Audio] To obtain the tabular summary of the total building horizontal stability moment and shear from EQX, we would choose Output, then, Global Results, then, Total Loads & Reactions, then, OK, and subsequently selecting the load case EQX to obtain the figures of 722,415 kilo Newton meter, and 34,400kN, respectively..

[Audio] The lateral deflection in x is obtained by choosing Contour Settings, then, Nodal Results, then, Displacements, then, Translation, U x to read the 28mm inelastic deflection at the top of the building for the chosen load case EQX. Thus, the elastic deflection is obtained by multiplying the displacement compatibility factor Cd of 3.85 to the inelastic deflection, to yield 108mm..

[Audio] Next, we could compute the seismic base moment in y from EQY by summing the effects of the axial force push-pull moment in y.. The axial force push-pull moment in y is obtained by choosing Contour Settings and/or Diagram Settings, then, Beam and Spring Element Results, then, Beam and Spring Forces and Moments, then, Axial Force, Fx to read the axial forces at the bottom of the column for the chosen load case EQY, which could then be multiplied by its lever arm of 30m, and summed to yield 218,580 kilo Newton meter push-pull moment, which tallies fairly well with the seismic base moment input of 210,000 kilo Newton meter..

[Audio] Next, we could compute the seismic base shear in y from EQY by summing the effects of the column shear in y, and the wall shear in y.. The column shear in y is obtained by choosing Contour Settings and/or Diagram Settings, then, Beam and Spring Element Results, then, Beam and Spring Forces and Moments, then, Shear Force, Fy to read the shear forces at the bottom of the column for the chosen load case EQY, which could then be summed to yield 8,340kN shear..

[Audio] The wall shear in y is obtained by choosing Contour Settings and/or Diagram Settings, then, Assembly Results, then, Assembly Forces and Moments, then, Assembly Force, Fz to read the wall shear force at the bottom of the wall for the chosen load case EQY, which could then be summed to yield 1,672kN shear force. The summation of the effects of the column shear in y, and the wall shear in y, is then computed as 10,012kN shear force, which tallies well with the seismic base shear input of 10,000kN..

[Audio] To obtain the tabular summary of the total building horizontal stability moment and shear from EQY, we would choose Output, then, Global Results, then, Total Loads & Reactions, then, OK, and subsequently selecting the load case EQY to obtain the figures of 210,210 kilo Newton meter, and 10,010kN, respectively..

[Audio] The lateral deflection in y is obtained by choosing Contour Settings, then, Nodal Results, then, Displacements, then, Translation, U y to read the 127mm inelastic deflection at the top of the building for the chosen load case EQY. Thus, the elastic deflection is obtained by multiplying the displacement compatibility factor Cd of 3.85 to the inelastic deflection, to yield 489mm..

[Audio] Next, the second method of structural analysis shall be conducted, i.e. the multi-modal response spectrum analysis method, using a high-ductility inelastic analysis approach, on a Shear and Core Wall (or Braced Frame) stabilized frame as Approach 1, and on a Moment Frame stabilized frame as Approach 2..

[Audio] In the multi-modal response spectrum analysis method, the response spectrum is defined by selecting Tree Tables, then, Dynamic Response, then, Response Spectra, then, choosing the seismic parameters of peak ground acceleration PGA of 40%g, importance factor of 1.00, soil response parameter or seismic coefficient of 1.10 and 1.60, behaviour factor or response modification factor of 5.50 (and thus defining the design spectrum), overstrength factor of 2.80 (not inserted herewith, manually assessed subsequently), and displacement compatibility factor of 3.85 (not inserted herewith, manually assessed subsequently). Note that the design inelastic spectrum cannot be defined by scaling the elastic spectrum by the response modification factor in the load case, or the load combination case, because the former may have a minimum high period, spectral acceleration plateau. Ensure that the default 5% of critical viscous damping is chosen so that no further scaling of the elastic response spectrum is inadvertently performed..

[Audio] Subsequently, the response spectrum analysis method is defined by selecting Analysis, then, New Analysis Task, then, Response Spectrum, defining the response spectrum for both horizontal directions, and the vertical direction for completion..

[Audio] Consequently, the earthquake load cases EQX and EQY within the loading combinations are defined by selecting Tree Tables, then, Cases and Tasks, then, Combination Cases, then, factor the response spectrum analysis load cases EQX and EQY (or analysis cases rather) within the EQ load combination cases, and reset factors pertinent to the equivalent static lateral force analysis method load cases to zero..

[Audio] Next, the mass for period calculations is defined by selecting Analysis, then, New Analysis Task, then, Modal Dynamic, then, Insert Mass Derived from Loads as say G + 0.3Q, to define 30% of the live load as contributing to the mass that affects, firstly, the structural natural periods, and secondly, the dynamic weight, in the dynamic excitation. Choose say 12 dynamic modes to participate in the multi-modal response analysis. Even if vertical modes and response are not being assessed, in either the multi-modal response spectrum analysis method, or the time history response analysis method, there is no option in the software to not include mass only for vertical modes. The option to add additional vertical restraint should thus not be used as it affects modes in all directions..

[Audio] To perform the overall 3D building analysis, modal eigenvalue analysis, and response spectrum analysis, we would choose Analysis, then, Analyse All..

[Audio] The fundamental modal periods in x and y are then obtained by selecting Output, then, Global Results, then, Dynamic Summary, then, OK to read the fundamental modal period in x as 0.55 seconds at 71% modal participating effective mass, and the fundamental modal period in y as 2.35 seconds at 87% modal participating effective mass, both similar to the reference assumptions. With the adopted say 12 dynamic modes, a cumulative participating mass percentage of 71% in x direction, and 97% in y direction is obtained, somewhat lesser than the usually acceptable threshold of 90%, due to the fact that some of the allocated 12 modes were vertical modes in this software run..

[Audio] The modal base shear in x is then obtained by selecting Output, then, Global Results, then, Response Spectrum Details, then, OK to ascertain the modes that are significant in terms of modal effective mass, and modal base shear. Here, both the contributions of modal effective mass, and modal base shear could be seen. A higher mode (i.e. of a lower period), which has a lower modal effective mass, could still yield a relatively high modal base shear, if it is subject to a higher spectral acceleration. The base shear coefficient in x is then obtained by dividing the summation of the modal base shears in x, by the total dynamic weight, and presented in terms of a percentage. Note that the figures here are presented in terms of inelastic responses, i.e. after the division by the response modification factor, R. The base shear coefficient is compared to the peak ground acceleration as a percentage of gravitational acceleration, to show how the soil dynamic characteristics, and structural dynamic characteristics, eventually affect the response..

[Audio] The modal base shear in y is then obtained by selecting Output, then, Global Results, then, Response Spectrum Details, then, OK to ascertain the modes that are significant in terms of modal effective mass, and modal base shear. Here, both the contributions of modal effective mass, and modal base shear could be seen. A higher mode (i.e. of a lower period), which has a lower modal effective mass, could still yield a relatively high modal base shear, if it is subject to a higher spectral acceleration. The base shear coefficient in y is then obtained by dividing the summation of the modal base shears in y, by the total dynamic weight, and presented in terms of a percentage. Note that the figures here are presented in terms of inelastic responses, i.e. after the division by the response modification factor, R. The base shear coefficient is compared to the peak ground acceleration as a percentage of gravitational acceleration, to show how the soil dynamic characteristics, and structural dynamic characteristics, eventually affect the response..

[Audio] The modal base shear in z is then obtained by selecting Output, then, Global Results, then, Response Spectrum Details, then, OK to ascertain the modes that are significant in terms of modal effective mass, and modal base shear. Here, both the contributions of modal effective mass, and modal base shear could be seen. A higher mode (i.e. of a lower period), which has a lower modal effective mass, could still yield a relatively high modal base shear, if it is subject to a higher spectral acceleration. The base shear coefficient in z is then obtained by dividing the summation of the modal base shears in z, by the total dynamic weight, and presented in terms of a percentage. Note that the figures here are presented in terms of inelastic responses, i.e. after the division by the response modification factor, R. The base shear coefficient is compared to the peak ground acceleration as a percentage of gravitational acceleration, to show how the soil dynamic characteristics, and structural dynamic characteristics, eventually affect the response..

[Audio] The floor acceleration in x could then be obtained by choosing Contour Settings, then, Nodal Results on Elements, then, Accelerations, then, Acceleration, A x to read the 2.8 metres per second square inelastic acceleration (i.e. 28% of gravitational acceleration), at the top of the building for the chosen load case response spectrum EQX..

[Audio] The floor acceleration in y could then be obtained by choosing Contour Settings, then, Nodal Results on Elements, then, Accelerations, then, Acceleration, A y to read the 1.1 metres per second square inelastic acceleration (i.e. 11% of gravitational acceleration), at the top of the building for the chosen load case response spectrum EQY..

[Audio] The floor acceleration in z could then be obtained by choosing Contour Settings, then, Nodal Results on Elements, then, Accelerations, then, Acceleration, A z to read the 8.1 metres per second square inelastic acceleration (i.e. 81% of gravitational acceleration), at the top of the building for the chosen load case response spectrum EQZ..

[Audio] All the effects computed before for the Equivalent Static Lateral Force Analysis Method, namely the base moment, base shear, and elastic deflections from EQX and EQY, can now be recalculated here for the Multi-Modal Response Spectrum Analysis Method, using the same procedures adopted in the previous section. For low rise or regular buildings, the magnitudes of the base moment and base shear effects, are generally lesser in the Multi-Modal Response Spectrum Analysis Method, compared to the Equivalent Static Lateral Force Analysis Method, because the modal effective mass of the dominant fundamental mode is only a proportion of the full dynamic mass, and higher modes, although subject to higher spectral accelerations, have lower participations. For high rise or irregular buildings, the magnitudes of the base moment and base shear effects, have the potential to be higher in the Multi-Modal Response Spectrum Analysis Method, compared to the Equivalent Static Lateral Force Analysis Method, because higher modes, although have lower participations, are still significant nevertheless, and are also subject to higher spectral accelerations..

[Audio] Next, the third method of structural analysis shall be conducted, i.e. the time history response analysis method, using a low-ductility elastic analysis approach, on a Shear and Core Wall (or Braced Frame) stabilized frame as Approach 3, and on a Moment Frame stabilized frame as Approach 3..

[Audio] In the time history response analysis method, the time history is defined by selecting Tree Tables, then, Dynamic Response, then, Load Curve, then, import an appropriate default time history, having matched it in the time domain to the defined elastic response spectrum, based upon the default 5% of critical viscous damping. Note that here, the units of the acceleration time history load factor, is effectively gravitational acceleration, "g". Ensure that the time history record time step has a delta-t of 0.02 seconds or lesser..

[Audio] Subsequently, the time history response analysis method is defined by selecting Analysis, then, New Analysis Task, then, Linear Time History, defining time history base accelerations for EQX and EQY, choosing Base Excitation in directions X, or Y as appropriate, with a scale factor of 1, and peak ground acceleration to scale the predefined Load Curve to the maximum magnitude of the specific acceleration time history record, herewith 4.7734 metres per second square. Ensure that the time history response analysis output time step has a delta-t of at most, a tenth of the highest mode of interest, say a tenth of 0.2 seconds, yielding 0.02 seconds or lesser. Also ensure that the time history response analysis duration is at least, 4 times the fundamental period, say 4 times 2.5 seconds, yielding 10.0 seconds or more..

[Audio] Consequently, the earthquake load cases EQX and EQY within the loading combinations are defined by selecting Tree Tables, then, Cases and Tasks, then, Combination Cases, then, envelope the time history analysis load cases EQX and EQY (or analysis cases rather) within the EQ load combination cases, and resetting factors pertinent to the equivalent static lateral force analysis method, and the response spectrum analysis method load cases to zero..

[Audio] Next, the mass for period calculations is defined by selecting Analysis, then, New Analysis Task, then, Modal Dynamic, then, Insert Mass Derived from Loads as say G + 0.3Q, to define 30% of the live load as contributing to the mass that affects, firstly, the structural natural periods, and secondly, the dynamic weight, in the dynamic excitation. Choose say 12 dynamic modes to participate in the time history response analysis. Even if vertical modes and response are not being assessed, in either the multi-modal response spectrum analysis method, or the time history response analysis method, there is no option in the software to not include mass only for vertical modes. The option to add additional vertical restraint should thus not be used as it affects modes in all directions..

[Audio] To perform the overall 3D building analysis, modal eigenvalue analysis, response spectrum analysis, and time history analysis, we would choose Analysis, then, Analyse All..

[Audio] The fundamental modal periods in x and y are then obtained by selecting Output, then, Global Results, then, Dynamic Summary, then, OK to read the fundamental modal period in x as 0.55 seconds at 71% modal participating effective mass, and the fundamental modal period in y as 2.35 seconds at 87% modal participating effective mass, both similar to the reference assumptions. With the adopted say 12 dynamic modes, a cumulative participating mass percentage of 71% in x direction, and 97% in y direction is obtained, somewhat lesser than the usually acceptable threshold of 90%, due to the fact that some of the allocated 12 modes were vertical modes in this software run..

[Audio] The floor acceleration in x could then be obtained by choosing Contour Settings, then, Nodal Results on Elements, then, Accelerations, then, Acceleration, A x to read the 16.0 metres per second square elastic acceleration (i.e. 160% of gravitational acceleration), at the top of the building for the chosen load case time history EQX..

[Audio] The floor acceleration in y could then be obtained by choosing Contour Settings, then, Nodal Results on Elements, then, Accelerations, then, Acceleration, A y to read the 8.1 metres per second square elastic acceleration (i.e. 81% of gravitational acceleration), at the top of the building for the chosen load case time history EQY..

[Audio] All the effects computed before for the Equivalent Static Lateral Force Analysis Method, and the Multi-Modal Response Spectrum Analysis Method, namely the base moment, base shear, and elastic deflections from EQX and EQY, can now be recalculated here for the Time History Response Analysis Method, using the same procedures adopted in the previous section. In this example, the Equivalent Static Lateral Force Analysis Method, and the Multi-Modal Response Spectrum Analysis Method were performed based on a high-ductility inelastic analysis approach, whereby a response modification factor of 5.5, was adopted. The Time History Response Analysis Method on the other hand was performed based on a low-ductility elastic analysis approach, whereby a response modification factor of 1.0, was adopted. The response magnitudes obtained from the Time History Response Analysis Method, could be verified by factoring the response magnitudes of the Equivalent Static Lateral Force Analysis Method, and the Multi-Modal Response Spectrum Analysis Method, by the response modification factor, and the damping correction factor where applicable, as shown herein..

[Audio] Let us now investigate the earthquake engineering loading definition, structural analysis and design, with the commercial software CSI Etabs 2020.3.0. Three methods of structural analysis shall be conducted, firstly the equivalent static lateral force analysis method, secondly the multi-modal response spectrum analysis method, and thirdly the time history response analysis method..

[Audio] First, the equivalent static lateral force analysis method, using a high-ductility inelastic analysis approach, shall be performed on a Shear and Core Wall (or Braced Frame) stabilized frame as Approach 1, and on a Moment Frame stabilized frame as Approach 2..

[Audio] CSC Orion R18 SP5, ProtaStructure 2018 SP4.0, or ProtaStructure 2019 SP7.0 are good geometrical modelling tools, and as such models could be best created in these software before converting the structural analytical model into CSI Etabs. This conversion could be done just by applying the Etabs Model Export tool to generate a Etabs e2k text file from ProtaStructure 2019 SP7.0. In this conversion, all finite elements geometries, sections properties, materials, applied (vertical) loads, and boundary conditions would be converted. Step 1 is to convert the model into an Etabs model. To generate an Etabs e2k text file, select ProtaStructure, then, Analysis, then, Building Analysis, then, Model Export Tab, then, Etabs Model Export. There are 2 export options to choose from, Option 1 being No Slab Panels, and Option 2 being With Slab Panels. To invoke Option 1, unclick the option to "Transfer Storey Slabs from Physical Model to generate a model in Etabs without slabs. And because there are no slabs exported, the slab loads are then decomposed onto beams, walls and columns prior to the conversion, hence generating a load decomposed model. Note that for this option to be valid, the slabs in ProtaStructure must not be meshed, failing which an erroneous result would ensue. To invoke Option 2, click the option to "Transfer Storey Slabs from Physical Model to generate a model in Etabs with slabs. And because there are now slabs exported, the slab loads are not decomposed onto beams, walls or columns prior to the conversion, hence generating a load undecomposed model. Note that in this option, if there were point, line or patch loads on the slabs, the slabs in ProtaStructure must indeed be meshed, failing which only uniform loads would be transferred. It is also acceptable that certain slabs are meshed in ProtaStructure whilst others are not meshed, so long as those with point, line or patch loads are indeed meshed..

[Audio] Step 2 is to open the model in Etabs by selecting CSI Etabs, then, File, then, Import, then, Etabs e2k Text File. Step 2 also involves the mandatory conversion of the slab meshing option from Auto Cookie Cut (which uses the yield line method) to Auto Mesh for a more accurate finite element based vertical load distribution. To change the slab meshing option, select CSI Etabs, then, Assign, then, Shell, then, Floor Auto Mesh Options, then, Selecting all Floors by Object Type, then, Default for Auto Meshing..

[Audio] Finally, Step 2 requires the mandatory integration of joints created to define slab point and line loads into the slab mesh. To integrate these joints into the mesh, select CSI Etabs, then, Assign, then, Joint, then, Joint Floor Meshing Options, then, Selecting all Joints by Object Type, then, Include Selected Joint Objects in Mesh. Note that, the point loads are still considered on the effects of the slab and subsequent supporting structure, even if this step is not performed. However, unless a rigid diaphragm is applied onto all the joints within the slab including these that define the point loads, or this step is performed, ill-conditioning error messages will ensue during the analysis..

[Audio] Step 3 is the mandatory modification of slab density to zero, as the self-weight loads are already decomposed onto the slab as slab area dead pressure loads during the conversion process. Slab density is set to zero by selecting CSI Etabs, then, Model Explorer, then, Model, then, Properties, then, Materials, then, choosing Slab Materials, then, Modify density to zero. At this stage, also check that all other materials referring to beams, columns and walls, are defined with an accurate concrete density of say, 25 kilo Newton per cubic metre, as often, the conversion results in density figures that are not precisely that..

[Audio] Step 4 is the mandatory modification of beam bending and torsional stiffness properties and slab bending stiffness properties. To modify beam bending stiffness properties, select CSI Etabs, then, Model Explorer, then, Model, then, Properties, then, Frame Sections, then, choosing Beam Sections, then, Property Modifiers, then, Set I22 and I33 to 0.70 (note J is 0.01). Note however that the beam elastic modulus in its material property would be factored down to 0.70 of its original magnitude, if the option to factor it down was chosen in ProtaStructure 2019 SP7.0 prior to conversion. Note that we had chosen to reduce the beam elastic modulus instead of the beam second moment of area in ProtaStructure 2019 SP7.0, simply due to a software error in ProtaStructure 2019 SP7.0, had the latter option been chosen. It would seem appropriate though to reset the beam elastic modulus in CSI Etabs to 1.0 (i.e. 100%) by selecting the Concrete Material Type in the Materials Property Dialog Box, and employ these bending or moment property modifiers instead. To modify slab bending stiffness properties, select CSI Etabs, then, Model Explorer, then, Model, then, Properties, then, Slab Sections, then, choosing Slab Sections, then, Property Modifiers, then, Set M11, M22 and M12 to 0.35..

[Audio] Step 5 is the mandatory definition of diaphragms for the application of horizontal loads. In the case of a [No Slab Panels Model], to define diaphragms, select firstly, CSI Etabs, then, Define, then, Diaphragms, then, Modify/Show Diaphragms, then, Define Rigid diaphragm D1 secondly, CSI Etabs, then, Assign, then, Joint, then, Diaphragms, then, Selecting all Joints except Support Joints at the base, then, Assign diaphragm D1 on joints at each floor In the case of a [With Slab Panels Model], to define diaphragms, select firstly, CSI Etabs, then, Define, then, Diaphragms, then, Modify/Show Diaphragms, then, Define Semi-Rigid diaphragm D1 secondly, CSI Etabs, then, Assign, then, Joint, then, Diaphragms, then, Selecting all Joints by Object Type, then, Disconnect diaphragm at all joints on all floors thirdly, CSI Etabs, then, Assign, then, Shell, then, Diaphragms, then, Selecting all Floors by Object Type, then, Assign diaphragm D1 on slabs at each floor fourthly, CSI Etabs, then, Assign, then, Joint, then, Diaphragms, then, Selecting all Joints by Object Type, then, Assign diaphragm From Shell Object on joints at each floor.

[Audio] The definition of diaphragms could be checked selecting the "Set Display Options", and selecting the "Diaphragm Extent" option..

[Audio] Step 6 is the mandatory definition and assignment of horizontal loads. To delete existing spurious horizontal loads from the conversion process, select CSI Etabs, then, Assign, then, Joint Loads, then, Force, then, Load Pattern Name, then, Selecting all Joints by Object Type, then, FX|FY | WX|WXY|WY|WYX | EQX|EQY, then, Delete Existing Loads. To define notional horizontal loads, select CSI Etabs, then, Define, then, Load Patterns, then, FX, FY, then, Type Notional, then, Auto Lateral Load = Auto, then, Modify Lateral Load, then, 0.015G in X and Y respectively..

[Audio] To define wind loads, select CSI Etabs, then, Define, then, Load Patterns, then, W X, W XY, W Y, W YX, then, Type Wind, then, Auto Lateral Load = User Loads, then, Modify Lateral Load, then, Insert figures for Fx and Fy including Ordinates respectively..

[Audio] To define earthquake loads, select CSI Etabs, then, Define, then, Load Patterns, then, EQX, EQY, then, Type Seismic, then, Auto Lateral Load = User Loads, then, Modify Lateral Load, then, Insert figures for Fx and Fy including Ordinates respectively..

[Audio] In the equivalent static lateral force analysis method, to check the magnitude and direction of the defined and assigned EQX, we would select CSI Etabs, then, Display, then, Load Assigns, then, Joint, then, Load Patterns = EQX, then, OK to display loads assignment..

[Audio] In the equivalent static lateral force analysis method, to check the magnitude and direction of the defined and assigned EQY, we would select CSI Etabs, then, Display, then, Load Assigns, then, Joint, then, Load Patterns = EQY, then, OK to display loads assignment..

[Audio] Next, the mass for period calculations is defined by selecting Define, then, Mass Source, then, Modify/Show Mass Source, then, select Specified Load Patterns, then, Insert Dead Load G Participation Factor as 1.0, and Live Load Participation Factor as say 0.3, to define 30% of the live load as contributing to the mass that affects the structural natural periods in the dynamic excitation. Deselect Lump Lateral Mass at Story Levels for no Diaphragm Dependency. Then, select Include Lateral Mass, and Include Vertical Mass, for the contribution of mass to affect both lateral and vertical vibration modes. If vertical modes and response are not being assessed, in either the multi-modal response spectrum analysis method, or the time history response analysis method, then the option to Include Vertical Mass may be deselected to reduce the required number of modes, but this should not be done as a matter of course. Finally, note that Element Self Mass should not be selected if Specified Load Patterns are selected, as the Load Pattern for "G" already contains a self-weight multiplier, otherwise resulting in the double-counting of self-mass..

[Audio] To perform the overall 3D building analysis, we would choose Analyze, then, Run Analysis..

[Audio] For the first output, we could compute the fundamental modal periods in x and y, by selecting Display, then, Deformed Shape, then, Displacement Resultant to read the fundamental modal period in x as 0.55 seconds, and the fundamental modal period in y as 2.43 seconds, both similar to the reference assumptions..

[Audio] The fundamental modal periods in x and y could also be obtained by selecting Model Explorer, then, Tables, then, Analysis Results, then, Structure Output, then, Modal Information, then, Table: Modal Participating Mass Ratios, then, Right-Click to Show Table to read the fundamental modal period in x as 0.55 seconds at 74% modal participating effective mass, and the fundamental modal period in y as 2.43 seconds at 87% modal participating effective mass, both similar to the reference assumptions..

[Audio] Next, we could compute the seismic base moment in x from EQX by summing the effects of the axial force push-pull moment in x, and the wall bending moment in x.. The axial force push-pull moment in x is obtained by choosing Display, then, Force/Stress Diagrams, then, Frame / Pier / Spandrel / Link Forces, then, Axial Force for Case = EQX to read the axial forces at the bottom of the column for the chosen load case EQX, which could then be multiplied by its lever arm of 30m, and summed to yield 389,700 kilo Newton meter push-pull moment..

[Audio] The wall bending moment in x is obtained by choosing Display, then, Force/Stress Diagrams, then, Frame / Pier / Spandrel / Link Forces, then, Moment 3-3 for Case = EQX to read the bending moment at the bottom of the wall for the chosen load case EQX, which could then be summed to yield 334,368 kilo Newton meter bending moment. The summation of the effects of the axial force push-pull moment in x, and the wall bending moment in x, is then computed as 724,068 kilo Newton meter bending moment, which tallies fairly well with the seismic base moment input of 722,000 kilo Newton meter..

[Audio] Next, we could compute the seismic base shear in x from EQX by summing the effects of the wall shear in x, and the column shear in x.. The wall shear in x is obtained by choosing Display, then, Force/Stress Diagrams, then, Frame / Pier / Spandrel / Link Forces, then, Shear 2-2 for Case = EQX to read the wall shear force at the bottom of the wall for the chosen load case EQX, which could then be summed to yield 32,694kN shear force..

[Audio] The column shear in x is obtained by choosing Display, then, Force/Stress Diagrams, then, Frame / Pier / Spandrel / Link Forces, then, Shear 2-2 for Case = EQX to read the shear forces at the bottom of the column for the chosen load case EQX, which could then be summed to yield 1,706kN shear. The summation of the effects of the wall shear in x, and the column shear in x, is then computed as 34,400kN shear force, which tallies well with the seismic base shear input of 34,400kN..

[Audio] To obtain the tabular summary of the total building horizontal stability moment and shear from EQX, we would choose Model Explorer, then, Tables, then, Analysis Results, then, Structure Output, then, Base Reactions, then, Table: Base Reactions, then, Right-Click to Show Table to read the figures of 722,415 kilo Newton meter, and 34,400kN, respectively..

[Audio] To obtain the graphical summary of the total building horizontal stability moment from EQX, we would choose Display, then, Storey Response Plots, then, Display Type as Overturning Moments, to show a graph of 722,415 kilo Newton meter base moment..

[Audio] To obtain the graphical summary of the total building horizontal stability shear from EQX, we would choose Display, then, Storey Response Plots, then, Display Type as Storey Shears, to show a graph of 34,400kN base shear..

[Audio] The lateral deflection in x is obtained by choosing Display, then, Deformed Shape, then, Displacement U X to read the 28mm inelastic deflection at the top of the building for the chosen load case EQX. Thus, the elastic deflection is obtained by multiplying the displacement compatibility factor Cd of 3.85 to the inelastic deflection, to yield 108mm..

[Audio] Next, we could compute the seismic base moment in y from EQY by summing the effects of the axial force push-pull moment in y.. The axial force push-pull moment in y is obtained by choosing Display, then, Force/Stress Diagrams, then, Frame / Pier / Spandrel / Link Forces, then, Axial Force for Case = EQY to read the axial forces at the bottom of the column for the chosen load case EQY, which could then be multiplied by its lever arm of 30m, and summed to yield 216,840 kilo Newton meter push-pull moment, which tallies fairly well with the seismic base moment input of 210,000 kilo Newton meter..

[Audio] Next, we could compute the seismic base shear in y from EQY by summing the effects of the column shear in y, and the wall shear in y.. The column shear in y is obtained by choosing Display, then, Force/Stress Diagrams, then, Frame / Pier / Spandrel / Link Forces, then, Shear 3-3 for Case = EQY to read the shear forces at the bottom of the column for the chosen load case EQY, which could then be summed to yield 8,520kN shear..

[Audio] The wall shear in y is obtained by choosing Display, then, Force/Stress Diagrams, then, Frame / Pier / Spandrel / Link Forces, then, Shear 3-3 for Case = EQY to read the wall shear force at the bottom of the wall for the chosen load case EQY, which could then be summed to yield 1,492kN shear force. The summation of the effects of the column shear in y, and the wall shear in y, is then computed as 10,012kN shear force, which tallies well with the seismic base shear input of 10,000kN..

[Audio] To obtain the tabular summary of the total building horizontal stability moment and shear from EQY, we would choose Model Explorer, then, Tables, then, Analysis Results, then, Structure Output, then, Base Reactions, then, Table: Base Reactions, then, Right-Click to Show Table to read the figures of 210,210 kilo Newton meter, and 10,010kN, respectively..

[Audio] To obtain the graphical summary of the total building horizontal stability moment from EQY, we would choose Display, then, Storey Response Plots, then, Display Type as Overturning Moments, to show a graph of 210,210 kilo Newton meter base moment..

[Audio] To obtain the graphical summary of the total building horizontal stability shear from EQY, we would choose Display, then, Storey Response Plots, then, Display Type as Storey Shears, to show a graph of 10,010kN base shear..

[Audio] The lateral deflection in y is obtained by choosing Display, then, Deformed Shape, then, Displacement U Y to read the 132mm inelastic deflection at the top of the building for the chosen load case EQY. Thus, the elastic deflection is obtained by multiplying the displacement compatibility factor Cd of 3.85 to the inelastic deflection, to yield 508mm..

[Audio] Next, the second method of structural analysis shall be conducted, i.e. the multi-modal response spectrum analysis method, using a high-ductility inelastic analysis approach, on a Shear and Core Wall (or Braced Frame) stabilized frame as Approach 1, and on a Moment Frame stabilized frame as Approach 2..

[Audio] In the multi-modal response spectrum analysis method, the response spectrum is defined by selecting Define, then, Functions, then, Response Spectrum, then, Add New Function, then, Choose Function Type to Add, then, choosing the seismic parameters of peak ground acceleration PGA of 40%g, importance factor of 1.00, soil response parameter or seismic coefficient of 1.10 and 1.60, behaviour factor or response modification factor of 5.50 (and thus defining the design spectrum), overstrength factor of 2.80 (not inserted herewith, manually assessed subsequently), and displacement compatibility factor of 3.85 (not inserted herewith, manually assessed subsequently). Note that the design inelastic spectrum cannot be defined by scaling the elastic spectrum by the response modification factor in the load case, or the load combination case, because the former may have a minimum high period, spectral acceleration plateau. Ensure that the default 5% of critical viscous damping is chosen so that no further scaling of the elastic response spectrum is inadvertently performed..

[Audio] Subsequently, choose Define, then, Load Cases, then, Modal, then, Modify/Show Case, then, Insert say 12 Dynamic Modes to participate in the multi-modal response analysis..

[Audio] Consequently, choose Define, then, Load Cases, then, Choosing EQX and EQY Modify/Show Case, then, Choose Load Case Type as Response Spectrum, then, Add Acceleration U1 and U2, with Function as the defined Response Spectrum herewith UBC 97, and Scale Factor as gravitational acceleration..

[Audio] Next, the mass for period calculations is defined by selecting Define, then, Mass Source, then, Modify/Show Mass Source, then, select Specified Load Patterns, then, Insert Dead Load G Participation Factor as 1.0, and Live Load Participation Factor as say 0.3, to define 30% of the live load as contributing to the mass that affects the structural natural periods in the dynamic excitation. Deselect Lump Lateral Mass at Story Levels for no Diaphragm Dependency. Then, select Include Lateral Mass, and Include Vertical Mass, for the contribution of mass to affect both lateral and vertical vibration modes. If vertical modes and response are not being assessed, in either the multi-modal response spectrum analysis method, or the time history response analysis method, then the option to Include Vertical Mass may be deselected to reduce the required number of modes, but this should not be done as a matter of course. Finally, note that Element Self Mass should not be selected if Specified Load Patterns are selected, as the Load Pattern for "G" already contains a self-weight multiplier, otherwise resulting in the double-counting of self-mass..

[Audio] To perform the overall 3D building analysis, modal eigenvalue analysis, and response spectrum analysis, we would choose Analyze, then, Run Analysis..

[Audio] The fundamental modal periods in x and y are then obtained by selecting Model Explorer, then, Tables, then, Analysis Results, then, Structure Output, then, Modal Information, then, Table: Modal Participating Mass Ratios, then, Right-Click to Show Table to read the fundamental modal period in x as 0.55 seconds at 74% modal participating effective mass, and the fundamental modal period in y as 2.43 seconds at 87% modal participating effective mass, both similar to the reference assumptions. With the adopted say 12 dynamic modes, a cumulative participating mass percentage of 91% in x direction, and 99% in y direction is obtained, more than the usually acceptable threshold of 90%..

[Audio] All the effects computed before for the Equivalent Static Lateral Force Analysis Method, namely base moment, base shear, and elastic deflections from EQX and EQY, can now be recalculated here for the Multi-Modal Response Spectrum Analysis Method, using the same procedures adopted in the previous section. For low rise or regular buildings, the magnitudes of the base moment and base shear effects, are generally lesser in the Multi-Modal Response Spectrum Analysis Method, compared to the Equivalent Static Lateral Force Analysis Method, because the modal effective mass of the dominant fundamental mode is only a proportion of the full dynamic mass, and higher modes, although subject to higher spectral accelerations, have lower participations. For high rise or irregular buildings, the magnitudes of the base moment and base shear effects, have the potential to be higher in the Multi-Modal Response Spectrum Analysis Method, compared to the Equivalent Static Lateral Force Analysis Method, because higher modes, although have lower participations, are still significant nevertheless, and are also subject to higher spectral accelerations..

[Audio] Next, the third method of structural analysis shall be conducted, i.e. the time history response analysis method, using a low-ductility elastic analysis approach, on a Shear and Core Wall (or Braced Frame) stabilized frame as Approach 3, and on a Moment Frame stabilized frame with additional damping as Approach 4..

[Audio] The nonlinear viscous dampers can be defined by selecting Define, then, Section Properties, then, Link / Support Properties, then, Add New Property, then, Define Link Type as Damper - Exponential, then, choose appropriate properties for damper damping coefficient, damper velocity exponent, and damper stiffness..

[Audio] Then, the nonlinear viscous dampers could be modelled by selecting Draw, then, Draw Link, then, model the nonlinear viscous dampers with the defined link property..

[Audio] In the time history response analysis method, the response spectrum is again defined in order to have a benchmark, to which the earthquake time history excitations can be scaled and matched onto. The response spectrum is defined by selecting Define, then, Functions, then, Response Spectrum, then, Add New Function, then, Choose Function Type to Add, then, choosing the seismic parameters of peak ground acceleration PGA of 40%g, importance factor of 1.00, soil response parameter or seismic coefficient of 1.10 and 1.60, behaviour factor or response modification factor of 5.50 (however inserted here as 1.0 for an elastic spectrum, as the response modification factor is not applicable in the performance-based time history response analysis method, where damping is explicitly modelled and defined), overstrength factor of 2.80 (not inserted herewith, again not applicable in the performance-based time history response analysis method, where assessment is already based on the elastic response of the structure), and displacement compatibility factor of 3.85 (not inserted herewith, again not applicable in the performance-based time history response analysis method, where assessment is already based on the elastic response of the structure). Ensure that the default 5% of critical viscous damping is chosen so that no further scaling of the elastic response spectrum is inadvertently performed..

[Audio] The time history can then be defined by selecting Define, then, Functions, then, Time History, then, Add New Function, then, Choose Function Type to Add as Matched to Response Spectrum, then, choosing an appropriate default time history, and matching it in the time domain to the defined elastic response spectrum. Ensure that the time history record time step has a delta-t of 0.02 seconds or lesser..

[Audio] Subsequently, choose Define, then, Load Cases, then, Modal, then, Modify/Show Case, then, Insert say 12 Dynamic Modes to participate in the time history response analysis, this being applicable only if a modal time history response analysis, as opposed to a direct time history response analysis, is performed..

[Audio] Consequently, choose Define, then, Load Cases, then, Choosing EQX and EQY Modify/Show Case, then, Choose Load Case Type as Time History, then, Choose Load Case Subtype as Nonlinear Modal "FNA" (also known as Fast Nonlinear Analysis), or Nonlinear Direct Integration, then, Add Acceleration U1 and U2, with Function as the defined response spectrum matched time history, and Scale Factor as gravitational acceleration. Ensure that the time history response analysis output time step has a delta-t of at most, a tenth of the highest mode of interest, say a tenth of 0.2 seconds, yielding 0.02 seconds or lesser. Also ensure that the time history response analysis duration is at least, 4 times the fundamental period, say 4 times 2.5 seconds, yielding 10.0 seconds or more..

[Audio] Next, the mass for period calculations is defined by selecting Define, then, Mass Source, then, Modify/Show Mass Source, then, select Specified Load Patterns, then, Insert Dead Load G Participation Factor as 1.0, and Live Load Participation Factor as say 0.3, to define 30% of the live load as contributing to the mass that affects the structural natural periods in the dynamic excitation. Deselect Lump Lateral Mass at Story Levels for no Diaphragm Dependency. Then, select Include Lateral Mass, and Include Vertical Mass, for the contribution of mass to affect both lateral and vertical vibration modes. If vertical modes and response are not being assessed, in either the multi-modal response spectrum analysis method, or the time history response analysis method, then the option to Include Vertical Mass may be deselected to reduce the required number of modes, but this should not be done as a matter of course. Finally, note that Element Self Mass should not be selected if Specified Load Patterns are selected, as the Load Pattern for "G" already contains a self-weight multiplier, otherwise resulting in the double-counting of self-mass..

[Audio] To perform the overall 3D building analysis, modal eigenvalue analysis, and time history response analysis, we would choose Analyze, then, Run Analysis..

[Audio] The fundamental modal periods in x and y are then obtained by selecting Model Explorer, then, Tables, then, Analysis Results, then, Structure Output, then, Modal Information, then, Table: Modal Participating Mass Ratios, then, Right-Click to Show Table to read the fundamental modal period in x as 0.55 seconds at 74% modal participating effective mass, and the fundamental modal period in y as 2.43 seconds at 87% modal participating effective mass, both similar to the reference assumptions. With the adopted say 12 dynamic modes, a cumulative participating mass percentage of 91% in x direction, and 99% in y direction is obtained, more than the usually acceptable threshold of 90%..

[Audio] The additional viscous damping in both directions are then obtained by selecting Display, then, Cumulative Energy Components, then, reading and scaling off the percentage figures for "NVD" over "GD", and multiplying them by the inherent viscous damping. This is done separately for EQX and EQY, which host the dynamic matched acceleration time history excitations. From this calculation, it can be seen that the additional viscous damping in direction Y, which is the only direction that the additional viscous dampers were modelled in, is 26.2% of critical, bringing the total viscous damping to 31.2% of critical in that direction..

[Audio] To obtain the graphical summary of the total building horizontal stability elastic moment and elastic shear, elastic deflections, and floor elastic accelerations from EQX, we could choose Display, then, Combined Storey Response Plots, to show a graph of 2,953 Mega Newton meter base moment, 130.3 Mega Newton base shear, 117mm elastic deflections at the top of the building, and 17.2 metres per second square elastic acceleration (i.e. 172% of gravitational acceleration), at the top of the building..

[Audio] To obtain the graphical summary of the total building horizontal stability elastic moment and elastic shear, elastic deflections, and floor elastic accelerations from EQY, we could choose Display, then, Combined Storey Response Plots, to show a graph of 392 Mega Newton meter base moment, 28.7 Mega Newton base shear, 234mm elastic deflections at the top of the building, and 4.7 metres per second square elastic acceleration (i.e. 47% of gravitational acceleration), at the bottom of the building..

[Audio] All the effects computed before for the Equivalent Static Lateral Force Analysis Method, and the Multi-Modal Response Spectrum Analysis Method, namely the base moment, base shear, and elastic deflections from EQX and EQY, can now be recalculated here for the Time History Response Analysis Method, using the same procedures adopted in the previous section. In this example, the Equivalent Static Lateral Force Analysis Method, and the Multi-Modal Response Spectrum Analysis Method were performed based on a high-ductility inelastic analysis approach, whereby a response modification factor of 5.5, was adopted. The Time History Response Analysis Method on the other hand was performed based on a low-ductility elastic analysis approach, whereby a response modification factor of 1.0, was adopted. The response magnitudes obtained from the Time History Response Analysis Method, could be verified by factoring the response magnitudes of the Equivalent Static Lateral Force Analysis Method, and the Multi-Modal Response Spectrum Analysis Method, by the response modification factor, and the damping correction factor where applicable, as shown herein..

[Audio] Let us now investigate the earthquake engineering loading definition, structural analysis and design, with the commercial software MidasGen 2019 version 2.1. Three methods of structural analysis shall be conducted, firstly the equivalent static lateral force analysis method, secondly the multi-modal response spectrum analysis method, and thirdly the time history response analysis method..

[Audio] First, the equivalent static lateral force analysis method, using a high-ductility inelastic analysis approach, shall be performed on a Shear and Core Wall (or Braced Frame) stabilized frame as Approach 1, and on a Moment Frame stabilized frame as Approach 2..

[Audio] CSC Orion R18 SP5, ProtaStructure 2018 SP4.0, or ProtaStructure 2019 SP7.0 are good geometrical modelling tools, and as such models could be best created in these software before converting the structural analytical model into MidasGen. This conversion could be done just by applying the Maverick Excel Convertor on the generated SAP2000 v15 text file from CSC Orion R18 SP5, ProtaStructure 2018 SP4.0, or ProtaStructure 2019 SP7.0. In this conversion, all finite elements geometries, sections properties, applied vertical loads (but not horizontal loads), and boundary conditions would be converted. Step 1 is to convert the model into a MidasGen model. To generate an MidasGen MGT text file, select ProtaStructure, then, Analysis, then, Building Analysis, then, Model Export Tab, then, choosing the SAP2000 v15 Data File, select SAP2000/Lusas Analysis Model Export, which is then taken through the Maverick Excel Convertor to generate a MidasGen MGT text file..

[Audio] Step 1 continues with opening the template Maverick MidasGen file in MidasGen, then, Tools, then, MGT Command Shell, then, Open and Select Midas-Text.txt, then, Run..

[Audio] Step 2 is the mandatory assignment of unassigned column material by dragging and dropping the chosen predefined material assignment. This is done by selecting MidasGen, then, Tree Menu, then, Works, then, Properties, then, selecting columns by unassigned material or section, then, Material, then, dragging and dropping the chosen predefined material assignment..

[Audio] Step 2 continues with the mandatory assignment of unassigned wall material by dragging and dropping the chosen predefined material assignment. This is done by selecting MidasGen, then, Tree Menu, then, Works, then, Properties, then, selecting walls by unassigned material or section, then, Material, then, dragging and dropping the chosen predefined material assignment. Note that by default, slabs, beams, and rigid beams materials are assigned with a pseudo material for zero density, as their self-weights have been decomposed (by default)..

[Audio] Step 3 is the mandatory modification of beam bending and torsional stiffness properties and slab bending stiffness properties. To modify beam bending and torsional stiffness properties, select MidasGen, then, Properties, then, Scale Factor, then, Section Stiffness Scale Factor, then, Replace to define cracked beam sections with Iyy and Izz as 0.70, and Ixx as 0.01 for no torsion..

[Audio] To modify slab bending stiffness properties, select MidasGen, then, Properties, then, Scale Factor, then, Plate Stiffness Scale Factor, then, selecting slabs by thickness property, then, Apply to define cracked beam sections with Mxx, Myy, and Mxy as 0.35..

[Audio] Step 4 is the mandatory definition of diaphragms for the application of horizontal loads. In MidasGen, diaphragms are defined as stories. Stories are defined for the purposes of applying storey-based lateral loads, of defining storey-based floor diaphragms, and of extracting storey-based displacement and stress (force) effects. To define stories, choose MidasGen, then, Structure, then, Control Data, then, Story, then, Auto Generate Story Data or manually define building stories from St00, St01, St02, etc, entering the floor centre coordinates for each floor as well for wind loads. Note that for an alternate automated storey definition for complex models with intermittent nodes between stories, in a temporary model, delete all vertical elements and associated free nodes, before Auto Generating the Story Data, and subsequently adding St00. Finally, note that storey diaphragms should not be considered for base floor St00 as support constraints have already been assigned, any particular floors with offset beams, and any other particular floors with X and/or Y nodal restraints..

[Audio] Step 5 is the mandatory definition and assignment of horizontal loads. To define notional horizontal loads, select MidasGen, then, Load, then, Static Loads, then, Nodal Body Force, then, Add to define notional loads NHL-X and NHL-Y as 0.015 of mass in X and Y respectively. Note that additional mass from dead loads is defined by choosing MidasGen, then, Load, then, Static Loads, then, Loads to Masses, then, Loads to Masses, then, Add All Load Types for Converting, and Load Cases LC-G-AREA, and LC-G-LINE..

[Audio] To define wind loads, select MidasGen, then, Load, then, Static Loads, then, Wind Loads, then, Add to specify user-defined wind loads W X, W XY, W Y, W YX, inserting figures for Fx and Fy..

[Audio] To define earthquake loads, select MidasGen, then, Load, then, Static Loads, then, Seismic Loads, then, Add to specify user-defined earthquake loads EQX, EQY, inserting figures for Fx and Fy..

[Audio] In the equivalent static lateral force analysis method, to check the magnitude and direction of the defined and assigned EQX, we would choose Tree Menu, then, Works, then, Static Loads, then, selecting LC-EQ-X, then, Display to display a vector diagram showing unique nodal loads in varying magnitudes and directions..

[Audio] In the equivalent static lateral force analysis method, to check the magnitude and direction of the defined and assigned EQY, we would choose Tree Menu, then, Works, then, Static Loads, then, selecting LC-EQ-Y, then, Display to display a vector diagram showing unique nodal loads in varying magnitudes and directions..

[Audio] Next, the mass for period calculations is defined by choosing Load, then, Static Loads, then, Loads to Masses, then, Loads to Masses, then, Add All Load Types for Converting, and Load Cases LC-G-AREA with participation factor 1.0, and LC-G-LINE with participation factor 1.0, and LC-Q with participation factor 0.3, to define 30% of the live load as contributing to the mass that affects the structural natural periods in the dynamic excitation. Note that Mass Direction should in general be X, Y, and Z.. This then naturally includes the contribution of mass to affect both lateral and vertical vibration modes. If vertical modes and response are not being assessed, in either the multi-modal response spectrum analysis method, or the time history response analysis method, then the option to include the vertical direction of mass may be deselected to reduce the required number of modes, but this should not be done as a matter of course..

[Audio] To perform the overall 3D building analysis, we would choose Analysis, then, Perform Analysis..

[Audio] For the first output, we could compute the fundamental modal periods in x and y, by selecting Results, then, Mode Shapes, then, Vibration Mode Shapes to read the fundamental modal period in x as 0.54 seconds, and the fundamental modal period in y as 2.31 seconds, both similar to the reference assumptions..

[Audio] The fundamental modal periods in x and y could also be obtained by selecting Results, then, Results Tables, then, Vibration Mode Shape to read the fundamental modal period in x as 0.54 seconds at 73% modal participating effective mass, and the fundamental modal period in y as 2.31 seconds at 87% modal participating effective mass, both similar to the reference assumptions..

[Audio] Next, we could compute the seismic base moment in x from EQX by summing the effects of the axial force push-pull moment in x, and the wall bending moment in x.. The axial force push-pull moment in x is obtained by choosing Results, then, Forces, then, Beam Diagrams, then, Fx for Case = EQX to read the axial forces at the bottom of the column for the chosen load case EQX, which could then be multiplied by its lever arm of 30m, and summed to yield 389,280 kilo Newton meter push-pull moment..

[Audio] The wall bending moment in x is obtained by choosing Results, then, Local Direction Force Sum, then, Mode as Line Select, then, choosing 2 points across the bottom of the wall and 1 point orthogonal to it, then, Calculate to read the 165,770 kilo Newton meter bending moment at the bottom of the wall for the chosen load case EQX, which could then be summed to yield 331,540 kilo Newton meter bending moment. Note that in MidasGen, the integration line is a design section cut line, and not a design strip cut line. The summation of the effects of the axial force push-pull moment in x, and the wall bending moment in x, is then computed as 720,820 kilo Newton meter bending moment, which tallies fairly well with the seismic base moment input of 722,000 kilo Newton meter..

[Audio] Next, we could compute the seismic base shear in x from EQX by summing the effects of the wall shear in x, and the column shear in x.. The wall shear in x is obtained by choosing Results, then, Local Direction Force Sum, then, Mode as Line Select, then, choosing 2 points across the bottom of the wall and 1 point orthogonal to it, then, Calculate to read the 16,584kN shear force at the bottom of the wall for the chosen load case EQX, which could then be summed to yield 33,168kN shear force. Note that in MidasGen, the integration line is a design section cut line, and not a design strip cut line..

[Audio] The column shear in x is obtained by choosing Results, then, Forces, then, Beam Diagrams, then, Fz to read the shear forces at the bottom of the column for the chosen load case EQX, which could then be summed to yield 1,228kN shear. The summation of the effects of the wall shear in x, and the column shear in x, is then computed as 34,396kN shear force, which tallies well with the seismic base shear input of 34,400kN..

[Audio] To obtain the tabular summary of the total building horizontal stability moment from EQX, we would choose Results, then, Results Tables, then, Story, then, Overturning Moment, then, select LC-EQ-X(ST) to read the figure of 722,415 kilo Newton meter..

[Audio] To obtain the tabular summary of the total building horizontal stability shear from EQX, we would choose Results, then, Results Tables, then, Reaction, then, select LC-EQ-X(ST) to read the figure of 34,400kN..

[Audio] The lateral deflection in x is obtained by choosing Results, then, Deformations, then, Displacement Contour, then, Dx to read the 28mm inelastic deflection at the top of the building for the chosen load case EQX. Thus, the elastic deflection is obtained by multiplying the displacement compatibility factor Cd of 3.85 to the inelastic deflection, to yield 108mm..

[Audio] Next, we could compute the seismic base moment in y from EQY by summing the effects of the axial force push-pull moment in y.. The axial force push-pull moment in y is obtained by choosing Results, then, Forces, then, Beam Diagrams, then, Fx for Case = EQY to read the axial forces at the bottom of the column for the chosen load case EQY, which could then be multiplied by its lever arm of 30m, and summed to yield 217,020 kilo Newton meter push-pull moment, which tallies fairly well with the seismic base moment input of 210,000 kilo Newton meter..

[Audio] Next, we could compute the seismic base shear in y from EQY by summing the effects of the column shear in y, and the wall shear in y.. The column shear in y is obtained by choosing Results, then, Forces, then, Beam Diagrams, then, Fy to read the shear forces at the bottom of the column for the chosen load case EQY, which could then be summed to yield 8,408kN shear..

[Audio] The wall shear in y is obtained by choosing Results, then, Local Direction Force Sum, then, Mode as Line Select, then, choosing 2 points across the bottom of the wall and 1 point orthogonal to it, then, Calculate to read the 800kN shear force at the bottom of the wall for the chosen load case EQY, which could then be summed to yield 1,600kN shear force. Note that in MidasGen, the integration line is a design section cut line, and not a design strip cut line. The summation of the effects of the column shear in y, and the wall shear in y, is then computed as 10,008kN shear force, which tallies well with the seismic base shear input of 10,000kN..

[Audio] To obtain the tabular summary of the total building horizontal stability moment from EQY, we would choose Results, then, Results Tables, then, Story, then, Overturning Moment, then, select LC-EQ-Y(ST) to read the figure of 210,210 kilo Newton meter..

[Audio] To obtain the tabular summary of the total building horizontal stability shear from EQY, we would choose Results, then, Results Tables, then, Reaction, then, select LC-EQ-Y(ST) to read the figure of 10,010kN..

[Audio] The lateral deflection in y is obtained by choosing Results, then, Deformations, then, Displacement Contour, then, Dy to read the 124mm inelastic deflection at the top of the building for the chosen load case EQY. Thus, the elastic deflection is obtained by multiplying the displacement compatibility factor Cd of 3.85 to the inelastic deflection, to yield 477mm..

[Audio] Next, the second method of structural analysis shall be conducted, i.e. the multi-modal response spectrum analysis method, using a high-ductility inelastic analysis approach, on a Shear and Core Wall (or Braced Frame) stabilized frame as Approach 1, and on a Moment Frame stabilized frame as Approach 2..

[Audio] In the multi-modal response spectrum analysis method, the response spectrum is defined by selecting Load, then, Dynamic Loads, then, RS Functions, then, Add, then, Design Spectrum, then, UBC(1997), then, choosing the seismic parameters of peak ground acceleration PGA of 40%g, importance factor of 1.00, soil response parameter or seismic coefficient of 1.10 and 1.60, behaviour factor or response modification factor of 5.50 (and thus defining the design spectrum), overstrength factor of 2.80 (not inserted herewith, manually assessed subsequently), and displacement compatibility factor of 3.85 (not inserted herewith, manually assessed subsequently). Note that the design inelastic spectrum cannot be defined by scaling the elastic spectrum by the response modification factor in the load case, or the load combination case, because the former may have a minimum high period, spectral acceleration plateau. Ensure that the default 5% of critical viscous damping is chosen so that no further scaling of the elastic response spectrum is inadvertently performed..

[Audio] Subsequently, choose Analysis, then, Eigenvalue, then, Insert say 12 Dynamic Modes to participate in the multi-modal response analysis..

[Audio] Consequently, choose Load, then, Dynamic Loads, then, RS Load Cases, then, define LC-EQ-X|Y-DESIGN, then, choose Function Name as the defined Response Spectrum Function, then, select Direction as horizontal X-Y or vertical Z, then, insert Excitation Angle as 0 degrees or 90 degrees, then, insert Scale Factor as 1.0..

[Audio] Next, the mass for period calculations is defined by choosing Load, then, Static Loads, then, Loads to Masses, then, Loads to Masses, then, Add All Load Types for Converting, and Load Cases LC-G-AREA with participation factor 1.0, and LC-G-LINE with participation factor 1.0, and LC-Q with participation factor 0.3, to define 30% of the live load as contributing to the mass that affects the structural natural periods in the dynamic excitation. Note that Mass Direction should in general be X, Y, and Z.. This then naturally includes the contribution of mass to affect both lateral and vertical vibration modes. If vertical modes and response are not being assessed, in either the multi-modal response spectrum analysis method, or the time history response analysis method, then the option to include the vertical direction of mass may be deselected to reduce the required number of modes, but this should not be done as a matter of course..

[Audio] To perform the overall 3D building analysis, modal eigenvalue analysis, and response spectrum analysis, we would choose Analysis, then, Perform Analysis..

[Audio] The fundamental modal periods in x and y could also be obtained by selecting Results, then, Results Tables, then, Vibration Mode Shape to read the fundamental modal period in x as 0.54 seconds at 73% modal participating effective mass, and the fundamental modal period in y as 2.31 seconds at 87% modal participating effective mass, both similar to the reference assumptions. With the adopted say 12 dynamic modes, a cumulative participating mass percentage of 90% in x direction, and 99% in y direction is obtained, more than the usually acceptable threshold of 90%..

[Audio] All the effects computed before for the Equivalent Static Lateral Force Analysis Method, namely the base moment, base shear, and elastic deflections from EQX and EQY, can now be recalculated here for the Multi-Modal Response Spectrum Analysis Method, using the same procedures adopted in the previous section. For low rise or regular buildings, the magnitudes of the base moment and base shear effects, are generally lesser in the Multi-Modal Response Spectrum Analysis Method, compared to the Equivalent Static Lateral Force Analysis Method, because the modal effective mass of the dominant fundamental mode is only a proportion of the full dynamic mass, and higher modes, although subject to higher spectral accelerations, have lower participations. For high rise or irregular buildings, the magnitudes of the base moment and base shear effects, have the potential to be higher in the Multi-Modal Response Spectrum Analysis Method, compared to the Equivalent Static Lateral Force Analysis Method, because higher modes, although have lower participations, are still significant nevertheless, and are also subject to higher spectral accelerations..

[Audio] Next, the third method of structural analysis shall be conducted, i.e. the time history response analysis method, using a low-ductility elastic analysis approach, on a Shear and Core Wall (or Braced Frame) stabilized frame as Approach 3, and on a Moment Frame stabilized frame with additional damping as Approach 4..

[Audio] The nonlinear viscous dampers can be defined by selecting Boundary, then, General Link, then, General Link Properties, then, Add, then, Define Application Type as Force Type Boundary Nonlinear Analysis, then, choose appropriate properties for damper damping coefficient, damper velocity exponent, and damper stiffness..

[Audio] Then, the nonlinear viscous dampers could be modelled by selecting Boundary, then, General Link, then, General Link, then, model the nonlinear viscous dampers with the defined link property..

[Audio] In the time history response analysis method, the time history is defined by selecting Load, then, Dynamic Loads, then, Time History Functions, then, Add Time Function, then, import an appropriate default time history, having matched it in the time domain to the defined elastic response spectrum, based upon the default 5% of critical viscous damping. Note that here, the units of the acceleration time history load factor, is effectively gravitational acceleration, "g". Ensure that the time history record time step has a delta-t of 0.02 seconds or lesser..

[Audio] Subsequently, choose Analysis, then, Eigenvalue, then, Insert say 12 Dynamic Modes to participate in the time history response analysis, this being applicable only if a modal time history response analysis, as opposed to a direct time history response analysis, is performed..

[Audio] Consequently, choose Load, then, Dynamic Loads, then, Time History Load Cases, then, define LC-EQ-X|Y-ELASTIC, then, choose Analysis Type as Nonlinear, and Analysis Method as Modal. Ensure that the time history response analysis output time step has a delta-t of at most, a tenth of the highest mode of interest, say a tenth of 0.2 seconds, yielding 0.02 seconds or lesser. Also ensure that the time history response analysis duration is at least, 4 times the fundamental period, say 4 times 2.5 seconds, yielding 10.0 seconds or more..

[Audio] Further, choose Load, then, Dynamic Loads, then, Ground Acceleration, then, define LC-EQ-X|Y-ELASTIC, then, choose Function Name as the defined Time History Function, then, insert Scale Factor as 1.0, then, insert Angle to Horizontal Ground Acceleration as 0 degrees for both x and y directions..

[Audio] Next, the mass for period calculations is defined by choosing Load, then, Static Loads, then, Loads to Masses, then, Loads to Masses, then, Add All Load Types for Converting, and Load Cases LC-G-AREA with participation factor 1.0, and LC-G-LINE with participation factor 1.0, and LC-Q with participation factor 0.3, to define 30% of the live load as contributing to the mass that affects the structural natural periods in the dynamic excitation. Note that Mass Direction should in general be X, Y, and Z.. This then naturally includes the contribution of mass to affect both lateral and vertical vibration modes. If vertical modes and response are not being assessed, in either the multi-modal response spectrum analysis method, or the time history response analysis method, then the option to include the vertical direction of mass may be deselected to reduce the required number of modes, but this should not be done as a matter of course..

[Audio] To perform the overall 3D building analysis, modal eigenvalue analysis, and time history response analysis, we would choose Analysis, then, Perform Analysis..

[Audio] The fundamental modal periods in x and y are then obtained by selecting Results, then, Results Tables, then, Vibration Mode Shape to read the fundamental modal period in x as 0.54 seconds at 73% modal participating effective mass, and the fundamental modal period in y as 2.31 seconds at 87% modal participating effective mass, both similar to the reference assumptions. With the adopted say 12 dynamic modes, a cumulative participating mass percentage of 90% in x direction, and 99% in y direction is obtained, more than the usually acceptable threshold of 90%..

[Audio] The floor acceleration in x could then be obtained by choosing Results, then, Deformations, then, Displacement Contour, then, Absolute Acceleration, then, Dx to read the 16.9 metres per second square elastic acceleration (i.e. 169% of gravitational acceleration), at the top of the building for the chosen load case time history EQX..

[Audio] The floor acceleration in y could then be obtained by choosing Results, then, Deformations, then, Displacement Contour, then, Absolute Acceleration, then, Dy to read the 4.7 metres per second square elastic acceleration (i.e. 47% of gravitational acceleration), at the bottom of the building for the chosen load case time history EQY..

[Audio] All the effects computed before for the Equivalent Static Lateral Force Analysis Method, and the Multi-Modal Response Spectrum Analysis Method, namely the base moment, base shear, and elastic deflections from EQX and EQY, can now be recalculated here for the Time History Response Analysis Method, using the same procedures adopted in the previous section. In this example, the Equivalent Static Lateral Force Analysis Method, and the Multi-Modal Response Spectrum Analysis Method were performed based on a high-ductility inelastic analysis approach, whereby a response modification factor of 5.5, was adopted. The Time History Response Analysis Method on the other hand was performed based on a low-ductility elastic analysis approach, whereby a response modification factor of 1.0, was adopted..

[Audio] And so that completes this lesson. Based on the seismic hazard assessment, and the soil response analysis, we had established codified earthquake response spectra. This is essentially the seismic hazard level at the surface of a particular site considering the bedrock hazard level, as well as the local soil conditions. Subsequently, three methods of earthquake structural analysis was investigated, the equivalent static lateral force analysis method, the multi-modal response spectrum analysis method, and the time history response analysis method. We then performed the methods of earthquake structural analysis on our 10-storey hypothetical reinforced concrete building using multiple commercial computer software programs, to structurally analyse the building, and in effect trace its vertical axial load take down, its horizontal building stability bending moment, and its horizontal building stability shear force. That's it for this lesson, I will see you at the next one..