1 A simple beam shown below is subjected to a distributed load that causesa maxi

Question

1 A simple beam shown below is subjected to a distributed load that causesa maximum moment of 15 k-ft on the section. For the section shown below with f 5 ksi and f 60 ksi 28 in. Sketch the strain and stress distributions for M-15 k-ft. Calculate values for: a) strain in top tensile steel b) strain in bottom tensile steel c) maximum tensile stress in concrete d) maximum tensile stress in steel e) maximum compressive stress in concrete Each longitudinal bar has an area of 0.44 in.2, for a total area of 2.64 in.2 Label the strains and stresses on your diagram. 23" 2" 3" 12" strains stresses

Explanation / Answer

Let the depth of neutral axis be xu .

Total compression = Total tension

0.36 fck b xu = 0.87 fy Ast

0.36 x 5 x 12 x xu = 0.87 x 60 x 2.64

xu = (0.87 x 60 x 2.64) / (0.36 x 5 x 12) = 6.38 in

a) Strain in top tensile steel = 0.0035 x (23 - 6.38) / 6.38 = 0.0091

b) Strain in bottom tensile steel = 0.0035 x (25 - 6.38) / 6.38 = 0.0102

c) Maximum tensile stress in concrete = 0

d) Maximum tensile stress in steel = 0.87fy = 0.87 x 60 ksi = 52.2 ksi

e) Maximum compressive stress in concrete = 0.446 fck = 0.446 x 5 ksi = 2.23 ksi

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