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homework1-2010 - Whitneys stress block as defined in the...

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University of Michigan Department of Civil and Environmental Engineering CEE – 615: Reinforced Concrete Members Winter 2010 Homework 1 Due: Thursday February 4, 2010 1) For the beam section shown below, determine the following points in the moment versus curvature response (section is under positive bending): a) First cracking b) Point between first cracking and first yield c) First yield (use both “exact” and approximate method) d) ε cm = 0.003 e) ε cm = 0.006 For modeling the concrete compression response, use Hognestad’s parabola with a linear descending tail. Use k 3 = 1 and Z = 150. 2) For the same section, calculate the moment and curvature corresponding to ε cm = 0.003 using Roy and Sozen’s bilinear model with a descending slope corresponding to Z = 150, as well as
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Unformatted text preview: Whitneys stress block as defined in the ACI Code. Compare your results with that obtained in part 1d). 3) If compression reinforcement with area equal to 25% of that of the tension steel is added to the section, what is the ultimate curvature capacity of the section based on the model used in Part 1? Use d = distance from extreme compression fiber to centroid of compression reinforcement = 2.5 in. Material properties: Concrete: f c = 4500 psi; co = 0.002; cu = 0.006 (ultimate strain capacity of concrete), w = 145 lb/ft 3 Steel: f y = 63 ksi; f su = 105 ksi; E = 29000 ksi; E sh = 1500 ksi; sh = 0.008; su = 0.12. 14 24 4 #8 21.5 Note: Compression reinforcement only for Part 3....
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  • Winter '09
  • parra
  • Compression Reinforcement, University of Michigan Department of Civil and Environmental Engineering, concrete compression response, linear descending tail

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