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Chapter 14: Q. 34 (page 385)

A 3.0-m-tall, 50-cm-diameter concrete column supports a 200,000 kg load. By how much is the column compressed?

Short Answer

Expert verified

The column is compressed by $1 m m$ .

Step by step solution

01

Given information

The radius of the concrete column is $r = \frac{50 c m}{2} = 25 c m = 0.25 m$

Mass of the load is $m = 200, 000 k g$

The length of the concrete column is $L = 3.0 m$

02

Compression produced in the column

The gravitational force on the load produces tensile stress $\frac{F}{A}$ , where $A$ is the cross-sectional area of the concrete column and $F$ is the gravitational force on the load.

Young's modulus given by $Y = \frac{\frac{F}{A}}{\frac{∆ L}{L}}$ .

The compression produced in the column is

$∆ L = \frac{F}{A} \frac{L}{Y} = \frac{m g}{{πr}^{2}} \frac{L}{Y} = \frac{200000 \times 9.8}{π {(0.25)}^{2}} \frac{3.0}{3 \times 10^{10}} = 1 m m$

Therefore, the column is compressed by $1 m m$ .

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