Question

A bolted joint is shown below. The maximum shear stress , in MPa, in the bolts at $A$ and $B$, respectively are

• A. $242.6,42.5$
• B. $42.5,242.6$
• C. $42.5,42.5$
• D. $60.15,343.64$

Answer 1

The correct option is A $242.6,42.5$


$F_A=F_B=F_C=\frac{10}{3}kN$
$F_A^{\prime }=\frac{P.e.r}{r_A^2+r_B^2+r_e^2}$
$=\frac{10\times {10}^3\times 150\times 40}{{40}^2+0^2+{40}^2}$
$F_A^{\prime }=18.75kN=F_C^{\prime }$
Shear load at A and C
$F_R=\sqrt{F_A^2+F_A^{12}}\Rightarrow \sqrt{{3.33}_A^2+{18.75}^2}$
$F_R=19.04kN$
${\tau }_{max}=\frac{19.04\times {10}^3}{\frac{\pi }{4}\times {10}^2}$
$({\tau }_{max}{)}_{A.C}=242.5MPa({\tau }_{max}{)}_B=42.44MPa$