Determine the shear stress at points B and C on the web of the beam located at section a-a.

Question

Accepted Answer

[latex]\bar{y}=\frac{(0.375)(4)(0.75)+(3.75)(6)(0.5)+(7.125)(2)(0.75)}{4(0.75)+6(0.5)+2(0.75)}=3.075 ext { in. } [/latex]

[latex]I=\frac{1}{12}(4)\left(0.75^{3} ight)+4(0.75)(3.075-0.375)^{2}[/latex]

[latex]\quad+\frac{1}{12}(0.5)\left(6^{3} ight)+0.5(6)(3.75-3.075)^{2}[/latex]

[latex]\quad+\frac{1}{12}(2)\left(0.75^{3} ight)+2(0.75)(7.125-3.075)^{2}[/latex]

[latex]=57.05 \mathrm{in}^{4}[/latex]

[latex]Q_{B}=\bar{y}_{B}^{\prime} A^{\prime}=2.7(4)(0.75)=8.1 \mathrm{in}^{3}[/latex]

[latex]Q_{C}=\bar{y}_{C}^{\prime} A^{\prime}=4.05(2)(0.75)=6.075 \mathrm{in}^{3} [/latex]

[latex] au=\frac{V Q}{I t} [/latex]

[latex] au_{B}=\frac{2800(8.1)}{57.05(0.5)}=795 \mathrm{psi}[/latex]

[latex] au_{C}=\frac{2800(6.075)}{57.05(0.5)}=596 \mathrm{psi}[/latex]

Question 7.74: Determine the shear stress at points B and C on the web of t...