A steel plate 50 mm wide is 5 mm thick and carries an in-plane bending moment. If the plate develops an elliptical crack of length 6 mm and width 2.4 mm calculate the maximum bending moment the plate can withstand if the fracture toughness of the steel is 3500 N/mm^3/2.

Question

A steel plate 50 mm wide is 5 mm thick and carries an in-plane bending moment. If the plate develops an elliptical crack of length 6 mm and width 2.4 mm calculate the maximum bending moment the plate can withstand if the fracture toughness of the steel is [latex] 3500 N / mm ^{3 / 2} [/latex].

Accepted Answer

For a plate of finite width

[latex] \alpha=[\sec (\pi a / w)]^{1 / 2} [/latex]

so that

[latex] \alpha=[\sec (3 \pi / 50)]^{1 / 2}=1.01 [/latex]

From Eq. (8.9)

[latex] K=K_{0} \alpha [/latex] (8.9)

[latex] K_{0}=3500 / 1.01=3465.3 [/latex]

Then, from Eq. (8.11)

[latex] K_{0}=\left(3 M a / 4 b^{3} ight)(\pi a)^{1 / 2} [/latex] (8.11)

[latex] 3465.3=\left(3 M imes 3 / 4 imes 1.2^{3} ight)(\pi imes 3)^{1 / 2} [/latex]

which gives

[latex] M=866.9 Nmm / ext { unit thickness } [/latex]

The maximum bending moment the plate can withstand is therefore

[latex] M_{\max }=866.9 imes 5=4334.5 Nmm [/latex]

Say

[latex] M_{\max }=4300 Nmm [/latex]

Question 8.10: A steel plate 50 mm wide is 5 mm thick and carries an in-pla...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions