Question

Two concrete spans of a 380 m long bridge are
placed end to end so that no room is allowed
for expansion. If the temperature increases by 20◦C, what
is the height to which the spans rise when
they buckle? Assume the thermal coefficient
of expansion is 1.2 × 10^−5(◦C)^−1
Answer in units of m.

Answer 1

Answer:

4.163 m

Explanation:

Since the length of the bridge is

L = 380 m

And the bridge consists of 2 spans, the initial length of each span is

$L_i = \frac{L}{2}=\frac{380}{2}=190 m$

Due to the increase in temperature, the length of each span increases according to:

$L_f = L_i(1+ \alpha \Delta T)$

where

$L_i = 190 m$ is the initial length of one span

$\alpha =1.2\cdot 10^{-5} ^{\circ}C^{-1}$ is the temperature coefficient of thermal expansion

$\Delta T=20^{\circ}C$ is the increase in temperature

Substituting,

$L_f=(190)(1+(1.2\cdot 10^{-5})(20))=190.0456 m$

By using Pythagorean's theorem, we can find by how much the height of each span rises due to this thermal expansion (in fact, the new length corresponds to the hypothenuse of a right triangle, in which the base is the original length of the spand, and the rise in heigth is the other side); so we find:

$h=\sqrt{L_f^2-L_i^2}=\sqrt{(190.0456)^2-(190)^2}=4.163 m$

Answer 2

The change in linear expansion is 0.045m

Data;

• L = 380m
• L1 = L/2 = 380/2 = 190m
• ΔT = 20°C
• L2 = ?

Linear Expansion

The linear expansion of a body can be calculated by using the formula

$L_2 = L_1 (1 + \alpha \delta T)$

Let's substitute the values and solve

$L_2 = L_1 (1+\alpha \delta T)\\L_2 = 190 (1 + (1.2*10^-^5*20))\\L_2 = 190.045m$

The height to which the spans rise is

$190.045 - 190 = 0.045m$

The change in linear expansion is 0.045m

Learn more on linear expansion here;

https://brainly.com/question/6985348