Assignment_4_SOLUTION - the design is complete with A s =A...

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Name: _ SOLUTION_ _ _ _ _ _ _ _ CE 441 Reinforced Concrete Design – Assignment 4 Due Thursday September 24, 2009 The elastic modulus of steel reinforcement is E s =29,000 ksi Help session is on Monday at 5:30-7:30 PM in CAMP 176 1. A rectangular concrete beam has a width of b =12 in. and an effective depth of d =27 in. The depth of compression steel A s from the compression face of the beam is d’ =3 in. as shown. Material strengths are f c ’=3.5 ksi and f y =60 ksi. The beam must carry a total factored bending moment of M u =600 k-ft. Design the flexural reinforcement for this beam at the tension controlled limit; i.e. ε t =0.005 when concrete reaches its limiting compressive strain of 0.003. Hint: Use the design procedure outlined in Lecture on 9-15-2009 as follows: (i) Determine A s1 and M n1 corresponding to ρ =0.6336 ρ b to obtain Φ =0.90. (ii) Compute M n ’=(M u /0.9)-M n1 , (iii) Assuming that A s ’ will yield at failure compute A s ’ and A s2 . (iv) Check if A s ’ actually yields at failure. If yes then
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Unformatted text preview: the design is complete with A s =A s1 +A s2 and A s ’ as computed in step (iii). (v) If A s ’ does not yield at failure, select actual bar sizes for A s ’ and check with the quadratic equation to compute the distance to the neutral axis c , the stress f s ’ , and the required value of A s ’ from M n ’=A s ’(f s ’-.85f c ’)(d-d’). If the required value of A s ’ is less than the actually provided value then the design is conservatively completed. 2. A beam has the same material properties and loading as in Problem 1. However, the effective depth of the beam is limited to d =21 in. due to architectural considerations. The width of the beam is increased to b =16 in. to improve the beam strength at the reduced effective depth. Design the flexural reinforcement for this beam at the tension controlled limit of ε t =0.005 as in Problem 1. Specify bar sizes to provide the required A s ’ and A s ....
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