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Chapter 12: Q82P (page 353)

If the (square) beam in fig 12-6aassociated sample problem is of Douglasfir, what must be its thickness to keep the compressive stress on it to16 of its ultimate strength?

Short Answer

Expert verified

The thickness of Douglas fir is, T=0.031 m

Step by step solution

01

Understanding the given information

The force exerted on the beam,F=7900 N(from sample problem of fig 12.6)

The Ultimate strength of Douglas fir, Su=50×106Nm2(From table 12.1)

02

Concept and formula used in the given question

You can use the concept of stress to find the thickness of Douglas fir. The formulas used are given below.

Stress=FAA=T2

03

Calculation for the thickness to keep the compressive stress on it to 16 of its ultimate strength

Rearranging the stress equation for area A, we get

A=FStress

But we have given that the compressive stress is 1/6 of the ultimate strength that is,

Stress=16Su

So, the equation for the area will become,

A=6FSu=6×7900 N50×106 N/m2=9.48×10−4m2

Now, the shape of Douglas fir is square, so its area is

A=T2

Hence, the thickness T is,

T=A=9.48×10−4m2=0.031 m

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Most popular questions from this chapter

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Figure:
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