   Chapter 2, Problem 2.5.4P Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
ISBN: 9781337093347
Textbook Problem

A steel rod. of 15-mm diameter is held snugly (but without am1 initial stresses) between rigid walls by the arrangement shown in the figure part a. (For the steel rod, use a = 12 X KT6fX and E = 200 GPa.)(a) Calculate the temperature drop AT (degrees Celsius) al which the average shear stress in the 12-mm diameter bolt becomes 45 MPa. Also, what is the normal stress in the rod?(b) What are the average bearing stresses in the bolt and clevis al A and between the washer {dw= 20 mm) and wall (r = IS mm) at £?(c) If the connection to the wall at B is changed to an end plate with two bolts (see figure part b), what is the required diameter dhof each bolt if the temperature drop is A J" = 38°C and the allowable bolt stress is 90 MPa? (a)

To determine

The temperature drop and normal stress in the rod.

Explanation

Given Information:

E=200GΡa

α=12×106/°C

dr=15mm

db=12mm

dw=20mm

twall=18mm

tc=10mm

ΔT=38°C

τb=45ΜΡa

Rod force P=α(ΔT)E×π4dr2

As Bolt is in double shear, shear stress in given by:

τ=</

(b)

To determine

The average bearing stress in the bolt and clevis at A and between the washer and the wall.

(c)

To determine

The diameter db of each bolt if temperature drop and maximum stress is given.

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