   Chapter 10, Problem 66AP

Chapter
Section
Textbook Problem

A 250-m-long bridge is improperly designed so that it cannot expand with temperature. It is made of concrete with α = 12 × 10−6 (°C)−1. (a) Assuming the maximum change in temperature at the site is expected to be 20°C, find the change in length the span would undergo if it were free to expand. (b) Show that the stress on an object with Young’s modulus Y when raised by ΔT with its ends Firmly fixed is given by a αY ΔT. (c) If the maximum stress the bridge can withstand without crumbling is 2.0 × 107 Pa, will it crumble because of this temperature increase? Young’s modulus for concrete is about 2.0 × 1010 Pa.

(a)

To determine
The change in length.

Explanation

Given info:

The length of the bridge is 250 m.

The co-efficient of linear expansion is 12×106/οC .

The maximum change in temperature is 20οC .

Formula to calculate the change in length is,

ΔL=αL0ΔT

• L0 is the length of the bridge.
• α is the co-efficient of linear expansion.
• ΔT is the change in temperature

(b)

To determine
The stress on the object.

(c)

To determine
The effect of the maximum stress applied.

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