Two structural members are connected together by a hinge which is formed as shown in Fig. P.7.19. The bolt is tightened up onto the sleeve through rigid end plates until the tensile force in the bolt is 10 kN. The distance between the head of the bolt and the nut is then 100 mm and the sleeve is

Question

Two structural members are connected together by a hinge which is formed as shown in Fig. P.7.19. The bolt is tightened up onto the sleeve through rigid end plates until the tensile force in the bolt is 10 kN. The distance between the head of the bolt and the nut is then 100 mm and the sleeve is 80 mm in length. If the diameter of the bolt is 15 mm and the internal and outside diameters of the sleeve are 20 and 30 mm, respectively, calculate the final stresses in the bolt and sleeve when an external tensile load of 5 kN is applied to the bolt.

Accepted Answer

The cross-sectional areas of the bolt and sleeve are

[latex] A_{ B }=\frac{\pi imes 15^{2}}{4}=176.7 mm ^{2}, A_{ S }=\frac{\pi\left(30^{2}-20^{2} ight)}{4}=392.7 mm ^{2} [/latex]

From equilibrium the compressive load in the sleeve must be equal to the tensile load in the bolt, therefore the stresses in the bolt and sleeve due to the tightening of the nut are

[latex]\begin{aligned}\sigma_{ B } &=\frac{10 imes 10^{3}}{176.7}=56.6 N / mm ^{2} \quad( ext { tension }) \\sigma_{ S } &=\frac{10 imes 10^{3}}{392.7}=25.5 N / mm ^{2} \quad( ext { compression })\end{aligned}[/latex]

When the external tensile load is applied the tensile stress in the bolt will be increased while the compressive stress in the sleeve will be reduced. Equations (7.38) apply in which Young’s modulus is the same for the bolt and sleeve so that, due to the 5 kN load

[latex]\sigma_{ S }=\frac{E_{ S }}{A_{ C } E_{ C }+A_{ S } E_{ S }} P \quad \sigma_{ C }=\frac{E_{ C }}{A_{ C } E_{ C }+A_{ S } E_{ S }} P[/latex] (7.38)

[latex] \sigma_{ B }=\frac{5 imes 10^{3}}{(176.7+392.7)}=8.8 N / mm ^{2} \quad( ext { tension })=\sigma_{ S } [/latex]

The final stresses are then

[latex]\begin{aligned}&\sigma_{ B }=56.6+8.8=65.4 N / mm ^{2} \&\sigma_{ S }=25.5-8.8=16.7 N / mm ^{2}\end{aligned} ext { (compression) }[/latex]

Question 7.19: Two structural members are connected together by a hinge whi...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions