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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 by1mm.

Step by step solution

01

Given information

The radius of the concrete column is r=50cm2=25cm=0.25m

Mass of the load is m=200,000kg

The length of the concrete column isL=3.0m

02

Compression produced in the column 

The gravitational force on the load produces tensile stress FA, where Ais the cross-sectional area of the concrete column and Fis the gravitational force on the load.

Young's modulus given by Y=FA∆LL.

The compression produced in the column is

∆L=FALY=mgπr2LY=200000×9.8π0.2523.03×1010=1mm

Therefore, the column is compressed by1mm.

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