2-2 The bolt shown in the figure is made of 2014-T6 aluminum alloy Young\'s modu
ID: 2996135 • Letter: 2
Question
2-2 The bolt shown in the figure is made of 2014-T6 aluminum alloy Young's modulus 10.6× 103 ksi) and is tightened so it compresses a cylindrical tube made of 1004-T61 magnesium alloy (Young's modulus 6.48x103 ksi). The tube has an outer radius of 1/2 in. and it is assumed that both the inner radius of the tube and the radius of the bolt are 1/4 in. The washers at the top and bottom of the tube are considered to be rigid and have a negligible thickness. Initially the nut is hand-tightened (until snug-fit). Then, by using a wrench, the nut is further tightened 1/2 turn. If the bolt has 20 threads per inch (means 20 turns to advance 1 inch), determine the stress developed in the bolt. 3 in. in in. in.Explanation / Answer
When a nut is tightened over a screw following stresses are induced:
(a) Tensile stresses due to stretching of the bolt
(b) Torsional shear stress due to frictional resistance at the threads.
(c) Shear stress across threads
(d) Compressive or crushing stress on the threads
(e) Bending stress if the surfaces under the bolt head or nut are not perfectly
normal to the bolt axis.
Since none of the above mentioned stresses can be accurately determined bolts
are usually designed on the basis of direct tensile stress with a large factor of
safety. The initial tension in the bolt may be estimated by an empirical relation
P1=284 d kN, where the nominal bolt diameter d is given in mm. The relation is
used for making the joint leak proof. If leak proofing is not required half of the
above estimated load may be used
so, P1 = 284*(1/2*2.54*10^-2) = 3.6068 KN
stress, z = P1/(pi*r^2) = (3.6068 * 10^3)/(pi*(1/2*2.54*10^-2)^2) = 7.118 Mpa
source: http://nptel.iitk.ac.in/courses/Webcourse-contents/IIT%20Kharagpur/Machine%20design1/pdf/Module-4_lesson-4.pdf
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