Semicircular grooves of radius r must be milled as shown

Chapter 4, Problem 4.63

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QUESTION:

Semicircular grooves of radius r must be milled as shown in the sides of a steel member. Using an allowable stress of 8 ksi, determine the largest bending moment that can be applied to the member when \(\text { (a) } r=\frac{3}{8} \text { in, (b) } r=\frac{3}{4} \text { in. }\)

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QUESTION:

Semicircular grooves of radius r must be milled as shown in the sides of a steel member. Using an allowable stress of 8 ksi, determine the largest bending moment that can be applied to the member when \(\text { (a) } r=\frac{3}{8} \text { in, (b) } r=\frac{3}{4} \text { in. }\)

ANSWER:

Step 1 of 5

According to the task, it is necessary to determine the maximum magnitude of the moment . Observing the cross-sectional shape, the required stress concentration  is read from Fig.4.25

The  ratio is required to read the value for

Step  2 of 5

For a)

And

We find out  as ,

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