2.51 A rod consisting of two cylindrical portions AB and BC is restrainedat both ends. Portion AB is made of steel (E, = 200 GPa, a, = 11.7 x10-6/°C) and portion BC is made of brass (E = 105 GPa, a = 20.9x 10-6/°C). Knowing that the rod is initially unstressed, determinethe compressive force induced in ABC when there is a temperaturerise of 50°C.250 mm300 mmFig. P2.51ABC30-mm diameter50-mm diameter

Given:- Portion AB is made of steelEs=200 GPaαs=11.7×10-6 /oCPortion BC is made of brassEb=105…

Answered: 2.51 A rod consisting of two…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

2.51 A rod consisting of two cylindrical portions AB and BC is restrained
at both ends. Portion AB is made of steel (E, = 200 GPa, a, = 11.7 x
10-6/°C) and portion BC is made of brass (E = 105 GPa, a = 20.9
x 10-6/°C). Knowing that the rod is initially unstressed, determine
the compressive force induced in ABC when there is a temperature
rise of 50°C.
250 mm
300 mm
Fig. P2.51
A
B
C
30-mm diameter
50-mm diameter

Expert Solution

Step 1

Given:-

$Portion AB is made of steel E_{s} = 200 GPa α_{s} = 11.7 \times 10^{- 6} /^{o} C Portion BC is made of brass E_{b} = 105 GPa α_{b} = 20.9 \times 10^{- 6} /^{o} C Rise of temperature, ΔT = 50^{o} C$

To find:-

Compressive force in ABC

Concept:-

Thermal expansion or contraction is given as

$ΔL = αΔTL Where ΔL = Thermal expansion or contraction α = Coefficient of thermal expansion ΔT = Change in temperature L = Length$

Expansion of contraction due to force P is

$ΔL = \frac{PL}{AE} Where ΔL = Expansion or contraction due to P P = Force L = Length A = Area of section E = Modulus of elasticity$

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