The beam supports a vertical shear of V = 7 kip. Determine the resultant force developed in segment AB of the beam.
Question 7.65: The beam supports a vertical shear of V = 7 kip. Determine t...
Section Properties:
I_{N A}=\frac{1}{12}(1)\left(5^{3}\right)+\frac{1}{12}(10)\left(0.5^{3}\right)=10.52083 \mathrm{in}^{4}Q=\bar{y}^{\prime} A^{\prime}=(0.5 y+1.25)(2.5-y)(0.5) \\ \quad=1.5625-0.25 y^{2}
Shear Flow:
q=\frac{V Q}{I} =\frac{7\left(10^{3}\right)\left(1.5625-0.25 y^{2}\right)}{10.52083} \\ \quad=\left\{1039.60-166.34 y^{2}\right\} \mathrm{lb/in}.
Resultant Shear Force: For web A B
V_{A B} =\int_{0.25 \mathrm{in} .}^{2.5 \mathrm{in} .} q d y=\int_{0.25 \mathrm{in} .}^{2.5 \mathrm{in.}}\left(1039.60-166.34 y^{2}\right) d y
=1474 \mathrm{lb}=1.47 \mathrm{kip}
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