Chapter 2: Analysis of Rectangular Prestressed Beam

Chapter 5: Footing.

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FOOTING A footing is the part of a building's foundation that distributes its weight across the ground. Footings are usually made of concrete, but can also be made of stone, brick, or wood. The common types of footing are the wall footing, isolated or single-column footing, combined footing, raft or mat, and pile caps..

413.3 Shallow Foundations 413.341 General 413.3.1.1 Minimum hase area of foundation shall be calculated from unfactored forces and moments transmitted by foundation to soil or rock and permissible bearing pressure selected through principles or soil or rock mechanics. 413.3.1.2 Overall depth of foundation shall be selected such that the effective depth of bottom reinforcement is at least 150 mm. 413.3.2 One-Way Shallow Foundations 413.3.2.1 The design and detailing of one-way shallow foundations, including strip footings, combined footings, and grade beams, shall be in accordance with this section and the applicable provisions of Sections 407and 409. 413.3.2.2 Reinforcement shall be distributed uniformly across entire width of one-way footings. 413.3.3 Two-Way Isolated Footings 413.3.3.1 The design and detailing of two-way isolated footings shall be in accordance with this section and the applicable provisions of Sections 407 and 408. 413.3.3.2 In square two-way fOotings, reinforcement shall be distributed uniformly across entire width of footing in both directions. 413.3.3.3 In rectangular footings, reinforcement shall be distributed in accordance with (a) and (b). a. b. Reinforcement in the long direction shall be distributed uniformly across entire width of footing. For reinforcement in the short direction, a portion of the total reinforcement, YsAs, shall be distributed uniformly over a band width equal to the length of short side of footing, centered on centerline of column or pedestal. Remainder of reinforcement required in the short direction,(l — ys)As, shall be distributed uniformly outside the center band width of footing, where y s is calculated by: 2 (413.3.3.3) where ß is the ratio of long to short side of footing..

Critical Section for Moment.

Critical Sections for Shear.

Critical Sections for Shear.

Critical Sections for Shear.

Isolated Footing.

Summary Pu qu Critical Moment Location: Face of column factored axial load Soil bearing capacity Wide-Beam Shear Location: d – distance from the face of column d Punching Shear Location: d/2 – distance from the face of column d/2 d/2 d/2 d/2 ∅ Rn ≥ Mu ∅ Vn ≥ Vu Vn = Vc + Vs with shear reinforcement Vn = Vc without shear reinforcement.

Isolated Footing Isolated footings are a type of foundation used to support individual columns or pillars. They are designed to distribute the load of the structure evenly across the soil beneath, minimizing the risk of settling or sinking. An isolated footing is used to support a single column's load. Its plan is usually square or rectangular. Square footings are used to reduce bending moments and shearing forces at critical sections..

Situation – Given the following data of a square column footing: Footing dimension: 2 m x 2 m Footing thickness, h = 620 mm Column dimension: 600 mm x 600 mm Main bars: 20 mm with fy = 275 MPa Concrete strength, f’c = 27.5 MPa Concrete cover = 75 mm Effective depth, d = 525 mm Column service dead load = 1800 kN Column service live load = 1200 kN 1. Compute the critical wide beam shear stress (MPa). 2. Compute the critical punching shear stress (MPa). 3. Determine the required number of 20 mm bars at critical moment. B = 2 m 0.6 B = 2 m 0.6 h = 620 Pu = 4,080 kN = 1.2(1800) + 1.6(1200) qu = Pu Afooting = 4,080 2(2) = 1,020 kPa Pu qu.

Situation – Given the following data of a square column footing: Main bars: 20 mm with fy = 275 MPa Concrete strength, f’c = 27.5 MPa Concrete cover = 75 mm Effective depth, d = 525 mm 1. Compute the critical wide beam shear stress (MPa). B = 2 m 0.6 B = 2 m 0.6 h = 620 4,080 kN 1,020 kPa d x ln.

Situation – Given the following data of a square column footing: Main bars: 20 mm with fy = 275 MPa Concrete strength, f’c = 27.5 MPa Concrete cover = 75 mm Effective depth, d = 525 mm 1. Compute the critical wide beam shear stress (MPa). h = 620 4,080 kN 1,020 kPa ln = (2 - 0.6)/2 = 0.70 m x = 0.70 – 0.525 = 0.175 m Vu = qu(B)(x) = 1,020(2)(0.175) = 357 kN Vu = Pu - qu(B)(B - x) = 4,080 - 1,020(2)(2 - 0.175) = 357 kN or vc = Vu ∅bw𝑑 = 357,000 0.75 (2,000)(525) Vu Pu = 0.453 MPa.

Situation – Given the following data of a square column footing: Main bars: 20 mm with fy = 275 MPa Concrete strength, f’c = 27.5 MPa Concrete cover = 75 mm Effective depth, d = 525 mm 2. Compute the critical punching shear stress (MPa). B = 2 m 0.6 B = 2 m 0.6 h = 620 4,080 kN 1,020 kPa d/2 d/2 d/2 d/2 c + d c + d.

Situation – Given the following data of a square column footing: Main bars: 20 mm with fy = 275 MPa Concrete strength, f’c = 27.5 MPa Concrete cover = 75 mm Effective depth, d = 525 mm 2. Compute the critical punching shear stress (MPa). h = 620 4,080 kN 1,020 kPa c + d = 0.6 + 0.525 = 1125 mm bo = 4(c + d) = 4 (1125) = 4,500 mm 4,080 kN Vu = Pu - qu(c+d)2 = 4,080 – 1,020(1.125)(1.125) = 2,789.062 kN vc = Vu ∅bo𝑑 = 2,789,062 0.75 (4,500)(525) = 1.574 MPa.

Situation – Given the following data of a square column footing: Main bars: 20 mm with fy = 275 MPa Concrete strength, f’c = 27.5 MPa Concrete cover = 75 mm Effective depth, d = 525 mm 3. Determine the required number of 20 mm bars at critical moment. B = 2 m 0.6 B = 2 m 0.6 h = 620 4,080 kN 1,020 kPa ln 𝐹 ln /2 F = qu(ln)(B) = 1,020(0.70)(2) = 1,428 kN Mu = F(ln/2) = 1,428(0.70/2) = 499.8 kN-m Rn = Mu ∅bd2 = 499.8𝑥106 0.9(2000)(525)2 = 1.007 MPa ρ = 0.85f′c fy (1- 1 − 2Rn 0.85f′c ) = 0.00374 ρmin = 1.4 fy = 0.00509 use this As = ρbd = 0.00509(2000)(525) = 5,344.5 mm2 N= As A20 = 5,344.5 π 4(20)2 = 17.012 use 18 bars.

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