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4. The section below (at right) shows a floor system consisting of T-beams that connect one-way slabs. Each T-beam has a span length, In, of 40 feet (i.e., in/out of the page). The T-beam cross-section and dimensions are shown in more detail at left. Complete parts a-c below. 2.5" a. Compute bf, the flange width, according to ACI318-19 requirements. Table 6.3.2.1 is shown below. Note: Sw represents the clear distance between webs. b. The neutral axis for this section is in the web. Compute the total area of steel, As, needed to resist bending in the beam. Compute the depth of the concrete compression area, a, for this section. C. 16" 6" As? 22" Wu 6.15 k/ft (including self weight); Mu = 1230 kft 8" Flange location Table 6.3.2.1-Dimensional limits for effective overhanging flange width for T-beams Each side of web One side of web 5 feet f'c = 3000 psi, p₁ = 0.85 fy = 60000 psi W₁ Effective overhanging flange width, beyond face of web Least of: Least of: 8h S₁/2 1₁/8 6h S₁/2 In/12 16"

4. The section below (at right) shows a floor system consisting of T-beams that connect one-way slabs. Each T-beam has a span length, In, of 40 feet (i.e., in/out of the page). The T-beam cross-section and dimensions are shown in more detail at left. Complete parts a-c below. 2.5" a. Compute bf, the flange width, according to ACI318-19 requirements. Table 6.3.2.1 is shown below. Note: Sw represents the clear distance between webs. b. The neutral axis for this section is in the web. Compute the total area of steel, As, needed to resist bending in the beam. Compute the depth of the concrete compression area, a, for this section. C. 16" 6" As? 22" Wu 6.15 k/ft (including self weight); Mu = 1230 kft 8" Flange location Table 6.3.2.1-Dimensional limits for effective overhanging flange width for T-beams Each side of web One side of web 5 feet f'c = 3000 psi, p₁ = 0.85 fy = 60000 psi W₁ Effective overhanging flange width, beyond face of web Least of: Least of: 8h S₁/2 1₁/8 6h S₁/2 In/12 16"

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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This is civil engineering concrete design practice. Everything needed is provided. Please answer all parts to the best of your ability. Provide thorough answer and explanation. This is only one question with a max of 3 parts due to guidelines. 

Centroid of a composite area y = Σy,Α; ΣΑ; First moment of area for a cross section Q = YA Moment of inertia for a rectangle, about neutral x-axis 1 = 1/2 bh³ f= Parallel axis theorem I = ΣĪ + Ad2 Linear stress distribution in a cross section All limits for design will be provided as part of the given information for each problem. My I Maximum moment for a simply supported beam under a distributed load Mmax n = W1² 8 Modular ratio Es Ec At ultimate, assumed compression force in a concrete section C = 0.85fc Ac For a rectangular section C = 0.85f ab, where a = At ultimate, assumed tension force in a concrete section T = Asfy Nominal moment for a concrete section Mn = T(d - y) = C(d - y) For a rectangular section Mn = T (d - ²) = C (d - 2) For a T-beam analysis M₁ = C, (d-+G(d-) = Asw fy (d − 2) + Assfy (d - 1/4) Percentage of reinforcing steel As bd Р From Aspbd, design capacity, фMn, is þMn pM₁ = opbd²fy (1-P) From the above equation, p is 0.85/2 (1 fy p = = B1C 1- Where Rn 1 = Mu obd² For doubly reinforced beams Mn = Asify (d-²) + As2fy (d-d') 2Rn 0.85 f Where Aszfy = A'sfs, and As = As1 + As2 Tensile strain Et = 0.003d-c C Strain in compression steel (doubly reinforced) c-d' € = 0.003- Yield strain (steel) = Ey E Load Factors (Ch5.3) U = 1.2D + 1.6L Modulus of rupture for a concrete cross section (Ch 19.2.3) fr = 7.52√ √f Minimum shrinkage and temperature reinforcement area (one-way slabs) = 0.0018bh As = Shear capacity φVn = φV€ + φV
Transcribed Image Text:Centroid of a composite area y = Σy,Α; ΣΑ; First moment of area for a cross section Q = YA Moment of inertia for a rectangle, about neutral x-axis 1 = 1/2 bh³ f= Parallel axis theorem I = ΣĪ + Ad2 Linear stress distribution in a cross section All limits for design will be provided as part of the given information for each problem. My I Maximum moment for a simply supported beam under a distributed load Mmax n = W1² 8 Modular ratio Es Ec At ultimate, assumed compression force in a concrete section C = 0.85fc Ac For a rectangular section C = 0.85f ab, where a = At ultimate, assumed tension force in a concrete section T = Asfy Nominal moment for a concrete section Mn = T(d - y) = C(d - y) For a rectangular section Mn = T (d - ²) = C (d - 2) For a T-beam analysis M₁ = C, (d-+G(d-) = Asw fy (d − 2) + Assfy (d - 1/4) Percentage of reinforcing steel As bd Р From Aspbd, design capacity, фMn, is þMn pM₁ = opbd²fy (1-P) From the above equation, p is 0.85/2 (1 fy p = = B1C 1- Where Rn 1 = Mu obd² For doubly reinforced beams Mn = Asify (d-²) + As2fy (d-d') 2Rn 0.85 f Where Aszfy = A'sfs, and As = As1 + As2 Tensile strain Et = 0.003d-c C Strain in compression steel (doubly reinforced) c-d' € = 0.003- Yield strain (steel) = Ey E Load Factors (Ch5.3) U = 1.2D + 1.6L Modulus of rupture for a concrete cross section (Ch 19.2.3) fr = 7.52√ √f Minimum shrinkage and temperature reinforcement area (one-way slabs) = 0.0018bh As = Shear capacity φVn = φV€ + φV
4. The section below (at right) shows a floor system consisting of T-beams that connect one-way slabs. Each T-beam has a span length, In, of 40 feet (i.e., in/out of the page). The T-beam cross-section and dimensions are shown in more detail at left. Complete parts a-c below. 2.5" a. Compute bf, the flange width, according to ACI318-19 requirements. Table 6.3.2.1 is shown below. Note: Sw represents the clear distance between webs. b. The neutral axis for this section is in the web. Compute the total area of steel, As, needed to resist bending in the beam. Compute the depth of the concrete compression area, a, for this section. C. 16" 6" As? 22" Wu = 6.15 k/ft (including self weight); Mu 1230 kft 8" Flange location Table 6.3.2.1-Dimensional limits for effective overhanging flange width for T-beams Each side of web One side of web 5 feet f'c = 3000 psi, B₁ = 0.85 fy = 60000 psi W₁ Effective overhanging flange width, beyond face of web Least of: Least of: 8h S₁/2 1₁/8 6h S₁/2 In/12 16"
Transcribed Image Text:4. The section below (at right) shows a floor system consisting of T-beams that connect one-way slabs. Each T-beam has a span length, In, of 40 feet (i.e., in/out of the page). The T-beam cross-section and dimensions are shown in more detail at left. Complete parts a-c below. 2.5" a. Compute bf, the flange width, according to ACI318-19 requirements. Table 6.3.2.1 is shown below. Note: Sw represents the clear distance between webs. b. The neutral axis for this section is in the web. Compute the total area of steel, As, needed to resist bending in the beam. Compute the depth of the concrete compression area, a, for this section. C. 16" 6" As? 22" Wu = 6.15 k/ft (including self weight); Mu 1230 kft 8" Flange location Table 6.3.2.1-Dimensional limits for effective overhanging flange width for T-beams Each side of web One side of web 5 feet f'c = 3000 psi, B₁ = 0.85 fy = 60000 psi W₁ Effective overhanging flange width, beyond face of web Least of: Least of: 8h S₁/2 1₁/8 6h S₁/2 In/12 16"
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