Given: While reinforced concrete beams are often rectangular or T-beam in shape, more exotic cross-sections are...

 

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Given: While reinforced concrete beams are often rectangular or T-beam in shape, more exotic cross-sections are possible and sometimes used because of the ability to cast concrete in any shape. Shown below is one such cross section, consisting of a triangle on top of a rectangular base. f'c = 2500 psi, Grade 60 steel Required: Assume that the Whitney stress block approach is valid for this cross-section (although some thought should be given to this assumption). 1) If the reinforcing steel consists of 4 - #9 bars, a) Assume that the reinforcing steel yields when the nominal moment capacity of the section, MN, is reached. Using the equilibrium approach introduced in class, solve for the depth of the compression stress block and the depth of the neutral axis. b) Solve for the nominal moment capacity (Mn) of this cross-section. c) Did the steel yield as assumed? 2) If the reinforcing steel consists of 4 ~ #4 bars, a) Assume that the reinforcing steel yields when the nominal moment capacity of the section, MN, is reached. Using the equilibrium approach introduced in class, solve for the depth of the compression stress block and the depth of the neutral axis. b) Solve for the nominal moment capacity (Mn) of this cross-section. c) Did the steel yield as assumed? 3) What area of tension reinforcement, As, will result in the compression stress block exactly ending at the bottom of the triangular part of the cross-section if the bars are Grade 40 vs Grade 60? MN Segment along length (only M shown) 0000 10 in 10 in X-Section 3 in 32 in Given: While reinforced concrete beams are often rectangular or T-beam in shape, more exotic cross-sections are possible and sometimes used because of the ability to cast concrete in any shape. Shown below is one such cross section, consisting of a triangle on top of a rectangular base. f'c = 2500 psi, Grade 60 steel Required: Assume that the Whitney stress block approach is valid for this cross-section (although some thought should be given to this assumption). 1) If the reinforcing steel consists of 4 - #9 bars, a) Assume that the reinforcing steel yields when the nominal moment capacity of the section, MN, is reached. Using the equilibrium approach introduced in class, solve for the depth of the compression stress block and the depth of the neutral axis. b) Solve for the nominal moment capacity (Mn) of this cross-section. c) Did the steel yield as assumed? 2) If the reinforcing steel consists of 4 ~ #4 bars, a) Assume that the reinforcing steel yields when the nominal moment capacity of the section, MN, is reached. Using the equilibrium approach introduced in class, solve for the depth of the compression stress block and the depth of the neutral axis. b) Solve for the nominal moment capacity (Mn) of this cross-section. c) Did the steel yield as assumed? 3) What area of tension reinforcement, As, will result in the compression stress block exactly ending at the bottom of the triangular part of the cross-section if the bars are Grade 40 vs Grade 60? MN Segment along length (only M shown) 0000 10 in 10 in X-Section 3 in 32 in