Answered: Find the extension of a steel rail of…

Find the extension of a steel rail of length 50 m if you have the following data: 2 Cross-sectional area = 4 cm, the tensile force acting = 2 80000 N, E for steel = 180x 10 N/m

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.4.16P: A round bar ABC of length 2L (see figure) rotates about an axis through the midpoint C with constant...

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Concept explainers

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial load acts perpendicular to the geometric cross-section of the component. Based on the direction of the application of the load, an axial load can be tensile or compressive. The analysis of bodies under the action of axial loads is generally studied under the branch of mechanics, known as statics.

Question

Find the extension of a steel rail of length 50 m if you
have the following data:
2
Cross-sectional area = 4 cm, the tensile force acting =
2
80000 N, E for steel = 180x 10 N/m

Expert Solution

Step 1

Given data:

The length of the steel rail is: $L_{s} = 50 m$ .

The cross-sectional area is: $A = 4 {cm}^{2} = 4 {cm}^{2} \frac{10^{- 4} m^{2}}{1 {cm}^{2}} {=4×10}^{- 4} m^{2}$

The tensile force is: $P_{t e n s i l e} = 80000 N$ .

The Young's modulus is $E_{s} = 180 \times 10^{9} \frac{N}{m^{2}}$

The expression to determine the value of the extension of the steel bar is,

$e = \frac{P_{t e n s i l e} L_{s}}{A E_{s}} . . . . . (1)$

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