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Determine the design moment capacity of the cross section by answering the sub-problems given below. The relevant cross section and material properties are given below. Given Properties fc = 6 ksi, b = 36 in, 2-1/2" typ 1 -36"- fy= d = 21.5 in = 60 ksi, A₂ = 1.41 in² 24" (a) Determine if the beam is over- or underreinforced. Double check your estimation by referring to Table A.4 in the textbook. (b) Given the answer of problem (a), draw the stress and strain distributions of the RC cross section at ultimate load. Use the rectangular stress block to describe the compression stress. Denote key stress/strain values using symbols. (c) Formulate the equilibrium equation. Also find the undetermined value a. (d) Determine the nominal and design moment capacity, Mn and Mu.

Determine the design moment capacity of the cross section by answering the sub-problems given below. The relevant cross section and material properties are given below. Given Properties fc = 6 ksi, b = 36 in, 2-1/2" typ 1 -36"- fy= d = 21.5 in = 60 ksi, A₂ = 1.41 in² 24" (a) Determine if the beam is over- or underreinforced. Double check your estimation by referring to Table A.4 in the textbook. (b) Given the answer of problem (a), draw the stress and strain distributions of the RC cross section at ultimate load. Use the rectangular stress block to describe the compression stress. Denote key stress/strain values using symbols. (c) Formulate the equilibrium equation. Also find the undetermined value a. (d) Determine the nominal and design moment capacity, Mn and Mu.

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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Determine the design moment capacity of the cross section by answering the sub-problems given below. The relevant cross section and material properties are given below.

Given Properties

(a) Determine if the beam is over- or underreinforced. Double check your estimation by referring to Table A.4.

(b) Given the answer of problem (a), draw the stress and strain distributions of the RC cross section at ultimate load. Use the rectangular stress block to describe the compression stress. Denote key stress/strain values using symbols.

(c) Formulate the equilibrium equation. Also find the undetermined value .

(d) Determine the nominal and design moment capacity, and .

TABLE A.4 Limiting steel reinforcement ratios for tension-controlled members fy, psi 40,000 60,000 80,000 100,000 fé Eu fy Eu+Ey+0.003 Calculated using &, = 0.002 "p=0.85 p₁- be fc, psi 3000 4000 5000 6000 7000 8000 9000 10000 3000 4000 5000 6000 7000 8000 9000 10000 3000 4000 5000 6000 7000 8000 9000 10000 3000 4000 5000 6000 7000 8000 9000 10000 B₁ 0.85 0.85 0.80 0.75 0.70 0.65 0.65 0.65 0.85 0.85 0.80 0.75 0.70 0.65 0.65 0.65 0.85 0.85 0.80 0.75 0.70 0.65 0.65 0.65 0.85 0.85 0.80 0.75 0.70 0.65 0.65 0.65 Pmax a 0.0220 0.0294 0.0346 0.0389 0.0423 0.0449 0.0505 0.0562 0.0135 0.0181 0.0213 0.0239 0.0260 0.0276 0.0311 0.0345 0.0093 0.0124 0.0146 0.0164 0.0178 0.0189 0.0213 0.0237 0.0069 0.0092 0.0108 0.0121 0.0132 0.0140 0.0158 0.0175 Pmin = 200 fy 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0020 0.0020 0.0020 0.0020 0.0020 0.0020 0.0020 0.0020 Pmin = 3√√fc fy 0.0041 0.0047 0.0053 0.0058 0.0063 0.0067 0.0071 0.0075 0.0027 0.0032 0.0035 0.0039 0.0042 0.0045 0.0047 0.0050 0.0021 0.0024 0.0027 0.0029 0.0031 0.0034 0.0036 0.0038 0.0016 0.0019 0.0021 0.0023 0.0025 0.0027 0.0028 0.0030
Transcribed Image Text:TABLE A.4 Limiting steel reinforcement ratios for tension-controlled members fy, psi 40,000 60,000 80,000 100,000 fé Eu fy Eu+Ey+0.003 Calculated using &, = 0.002 "p=0.85 p₁- be fc, psi 3000 4000 5000 6000 7000 8000 9000 10000 3000 4000 5000 6000 7000 8000 9000 10000 3000 4000 5000 6000 7000 8000 9000 10000 3000 4000 5000 6000 7000 8000 9000 10000 B₁ 0.85 0.85 0.80 0.75 0.70 0.65 0.65 0.65 0.85 0.85 0.80 0.75 0.70 0.65 0.65 0.65 0.85 0.85 0.80 0.75 0.70 0.65 0.65 0.65 0.85 0.85 0.80 0.75 0.70 0.65 0.65 0.65 Pmax a 0.0220 0.0294 0.0346 0.0389 0.0423 0.0449 0.0505 0.0562 0.0135 0.0181 0.0213 0.0239 0.0260 0.0276 0.0311 0.0345 0.0093 0.0124 0.0146 0.0164 0.0178 0.0189 0.0213 0.0237 0.0069 0.0092 0.0108 0.0121 0.0132 0.0140 0.0158 0.0175 Pmin = 200 fy 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0050 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0020 0.0020 0.0020 0.0020 0.0020 0.0020 0.0020 0.0020 Pmin = 3√√fc fy 0.0041 0.0047 0.0053 0.0058 0.0063 0.0067 0.0071 0.0075 0.0027 0.0032 0.0035 0.0039 0.0042 0.0045 0.0047 0.0050 0.0021 0.0024 0.0027 0.0029 0.0031 0.0034 0.0036 0.0038 0.0016 0.0019 0.0021 0.0023 0.0025 0.0027 0.0028 0.0030
Determine the design moment capacity of the cross section by answering the sub-problems given below. The relevant cross section and material properties are given below. Given Properties fc = 6 ksi, b = 36 in, 2-1/2" typ 1 -36"- fy= d = 21.5 in = 60 ksi, A₂ = 1.41 in² 24" (a) Determine if the beam is over- or underreinforced. Double check your estimation by referring to Table A.4 in the textbook. (b) Given the answer of problem (a), draw the stress and strain distributions of the RC cross section at ultimate load. Use the rectangular stress block to describe the compression stress. Denote key stress/strain values using symbols. (c) Formulate the equilibrium equation. Also find the undetermined value a. (d) Determine the nominal and design moment capacity, Mn and Mu.
Transcribed Image Text:Determine the design moment capacity of the cross section by answering the sub-problems given below. The relevant cross section and material properties are given below. Given Properties fc = 6 ksi, b = 36 in, 2-1/2" typ 1 -36"- fy= d = 21.5 in = 60 ksi, A₂ = 1.41 in² 24" (a) Determine if the beam is over- or underreinforced. Double check your estimation by referring to Table A.4 in the textbook. (b) Given the answer of problem (a), draw the stress and strain distributions of the RC cross section at ultimate load. Use the rectangular stress block to describe the compression stress. Denote key stress/strain values using symbols. (c) Formulate the equilibrium equation. Also find the undetermined value a. (d) Determine the nominal and design moment capacity, Mn and Mu.
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