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Assignment_1_SOLUTION - Name SOLUTION CE 441 Reinforced...

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Name: _ _ SOLUTION_ _ _ _ _ _ _ _ CE 441 Reinforced Concrete Design – Assignment 1 Due Thursday September 3, 2009 The stress-strain ( f - ε ) relationship for a certain concrete from a 28th-day uniaxial compression test is determined to be represented by the equation f (ksi)=4,000 ε – 1.0x10 6 ε 2 as shown in the figure. A beam of rectangular cross section with height h =24 inches and width b =10 inches is made of this concrete with three #9 bars as tension reinforcement (A s =3.0 in 2 from ACI318-08 p 439), located at d=21.0 in. The modulus of elasticity of steel bars is E=29,000 ksi and the yield strength is F y =60 ksi. Please answer the following questions and carry out the required analysis: (a) What is the 28-day compressive strength f c ' for this concrete? (b) Assume that the tension steel A s will reach its yield strain ε y before the concrete reaches its maximum strain of 0.003 (to be verified later in part (e)). Draw the linear strain diagram acting on the cross section for ε s = ε y and using similar triangles write the strain ε at distance y (+
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