UNIVERSITY
OF CALGARY
ENGG 317 MECHANICS OF SOLIDS
FINAL EXAM
Date: Thursday April 25, 2002
W1NTER.
2002 Tlme: 15:30-18:30
Instructions to the candidates:
Write your name and m on the secondpage. The exam is closed book and of 3 hours maximum duration. Scientific calculators are allowed. Maximum maIks for each question are shown in brackets. Answer all 6 questions. Useful fonnulae are provided on the last page of the exam booklet. The University of Calgary Examination Rules apply.
(i1J
ENGG 317 Final Exam Winter 2002
1. Consider the famous leaning Pisa tower with an inclination of Q ~s to the vertical. The structuraJ core of the tower consists of masonry and may be regardedas a cylinder of height H = 55 m, with outer diameter VI = 19.6 In. and inner diameter ~ = 19 m. The weight of the tower, estimated at W =165 MN, is assumedto be unifonnly distributed along its height. and acts at the centre of gravity at mid height The baseof the tower is consideredrigidly fixed to its foundation.
Fi~
1: Pisatower
(shear
(a) In a section denoted by A.A shown in the figure below, detennine the internal fo~s force, bending moment and axial fo~e) in tenns of W, Q and H. [3 marks]
(b) Determine the maximum pennissible inclination a such that there are no tensile nomla1 stresses Us developedin the tower. [4 marks] (c) For the angle found in (a), determine the maximum compressivenonna] stressUz in the lower. [3 marks]
SNOO WInter
317 FInal Exam 2002
.07
_06
2. A steel circular tube of outer diameter of 70 mm and inner diameter 60 mm acts as a spreaderin the pipe hoisting system shown below. The spreaderis 2.5 m long and has a modulus of elasticity of 210 GPa. The cables are securedat both ends of the spreaderthrough pinned connections. The pipe is flexible and held by meansof collars and cables with also pinned connections. The weight W of the pipe is assumedto be 1mif0000ydistriOOted over its entire length and can be representedby the distributed load w shown below.
;<,;.(j %
(Q)
q
~
Figure 2: Hoistjng system
I;A)
(a) What is the maximIDn weight W of pipe that can be lifted if a factor of safety(SF) of 2 is
retained against buckling of the spreader?Note that the SF
= (Pool Palloou) where
Per is the
Cl!!ticalload dctcrmiDCd BuJcr's by fOnmJIa ~-ended for
bar!!!_~~ion.
[6_marks]
J\
L
(b) For a givenw, de=mine the maximum deflection the pipe and the rotationof the co.l~ of duringlifting, ~ defonncdshape thepipe in the figure below. In your calculations, of leave your answers tcnnsof the y=-
TL
GJ
" Mwz (""- 1 \as . I0 ad ) +--L\1'-~ ye nc Ing
A
Is
111
0'. BENDINO BEAM EQUATIONS
-~
EI~
(pureclasticbending)
-M(x)
EULER'S BUCKLING EQUATION
~EI Per = L2
PRESSURE VESSELS
0'1
pr - T;
0'2'= pr
2t
MOMENTS OF INERTIA
J
~
(polarmoment ineniafor c~le) of
of inertia about % axis for a c~le)
~(monat 4
I. = ~(moment
of inertia about z axis for a rectangle)
1= Ic + AJfJ g=~ fA dA
RGW/rgw