Assignment_5_SOLUTION - s ’ is needed proceed as follows...

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Name: _ _SOLUTION _ _ _ _ _ _ _ _ _ _ CE 441 Reinforced Concrete Design – Assignment 5 Due Thursday October 8, 2009 1. For the T-beam section determine the balanced steel area A sb . Check to see if the actual A s =five #10 bars is within the minimum limit according to ACI 10.5.1. Verify also that the tensile strain ε t in the steel is at least 0.004 when concrete reaches its maximum compressive strain of 0.003. Determine the nominal flexural strength M n and the strength reduction factor Φ . Use f c '=4,000 psi, f y =60,000 psi, and E s =29,000,000 psi. 2. For the cross-section shown determine the balanced steel area A sb . Check to see if the actual A s = five # 9 bars is within the minimum limit according to ACI 10.5.1. Check also if the section satisfies ACI 10.3.5; i.e. ε t is to be no less than 0.004 at nominal strength M n . If ACI 10.3.5 is not satisfied, add sufficient A s ’ to increase ε t to at least 0.004. If A
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Unformatted text preview: s ’ is needed, proceed as follows: ( i ) determine the distance c to the neutral axis corresponding to ε t =0.004 and compute the total compressive force C c produced by concrete for this case. ( ii ) Assuming that A s ’ will yield, determine the required A s ’ to provide sufficient additional compressive force C s such that equilibrium is satisfied by T = C c + C s . ( iii ) Select a pair of bars for A s ’ and check if the provided A s ’ yields at failure. ( iv ) If A s ’ yields, compute the depth of the stress block a using equilibrium ( Σ F x =0) with f s ’= f y ; if A s ’ does not yield, write the quadratic equilibrium equation in terms of c , and solve for c . Assume d ’=3 in. from the very top of the beam. Determine the nominal flexural strength M n and the strength reduction factor Φ . Use f c '=4,000 psi, f y =60,000 psi, and E s =29,000,000 psi....
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