Question

A 15-ft solid concrete cantilever beam with a rectangular cross-section is shown below. It supports a load w = 2,150 lb/ft. The concrete has a tensile strength of 650 psi and a compressive strength of 6,000 psi. (a) Determine the maximum tensile and compressive stresses in the beam due to the applied load (b) Explain where failure would initiate in the solid concrete beam under the applied load. (c) Because the solid concrete beam is not adequate to carry the load, you give two op- tions for new designs for the beam. Design Option 1 includes the addition of steel reinforcement (rebar). Explain where in the cross-section you would place the rebar and why. (d) Design Option 2 includes prestressing the beam. Determine the minimum compression force, P, needed to place the entire cross-section in compression. Parts () - Beam Crow-oction 15 12 in Parts 8 in 15

Answer 1

W=2150 lbfE ܝܠ ܝܐ ܝܠ ܀ 4 12 in K sin marimum moment due to vol in generated at the support and the bending is given by 쓸 feel H: 3 wx 2 x So, at 2:0 ; M=0 1= 15; M = 2150 X15X 15 241875 647 hat moment of thestia of the section = BD3 -1152 mch 12 So, stress generated will be given by. Me fi z 'where fa fletusal stress z = section modulus = I I f = m m 241875 X 12 X 6 15117 118 Iblinch? 1152 = 15117.18 psi = 650 psi Given in question, Tensile strength of beam compressive strength of becm= 6000 PS; But the flexural stress calculated is greater than above two Hence the beam fails. The farluse will occur at or near the support, because it is the portion where due to maumum neobandingamax th Compression & Tension will occur. Scanner

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