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Unformatted text preview: I) l} mks mks l0
mks mks NAME;
UNIVERSITY OF TORONTO
FACULTY OIT APPLIED SCIENCE AND ENGINEERING
FINAL EXAMINATIONS. DECEMBER ZOOI First Year  Program 5 CW IOZHH‘  STRUCTURES AND MATERIALS Examiners  M P. Collins and WM. Onsongo Pemiissihle Aids: notebook. calculator and drafting instruments Through the miracle ol'time travel you ﬁnd yourself in Spain duri1.~_.j_'l'ra_ian‘s reign. You are
assisting Caius Julius Lacer design his great bridge across the Tagus River. He is concerned that
during construction ofthe bridge. when the granite block piers are standing alone. a severe spring
llood may damage or even destroy these stone towers. He asks you to check the tallest central pier
for 2: river depth of 28 m and a river Speed of6 mfsee. (a) lfthe granite blocks weigh 26 kam'1 in airt what will he the uniform compressive stress in the
masonry at the base ofthe 40 m high pier caused by selfweight when the river depth is 3 m’.’ (b) lithe sharp “cutwater" on the pier reduces the drag coefﬁcient to 0.85 what will be the
uniform horizontal pressure caused by the 6 misec river velocity? Water has a densin of
1000 ngm3. (c) What is the moment at the base oIthe tower caused by the water pressure'.’ Will this moment
cause the blocks on the upstream side ofthe pier to separate? (d) Estimate the river velocity. at a river depth 0(28 m. which would destroy this stone block
bridge pier. Cvar .
Dehi'u
= 25,
I
94:)
Rtvﬁrl . , . i
s .4 '   '9 hi. ‘3_ '7 Page 1 of 8 H H LI 0 Page 2 of8 {) H H H l J The steel truss shown below supports a point load of 300 kN applied at joint E IO (a) Calculate the axial force in each member ofthe truss clue to the 300 kN loads Write your
:‘nks calculated forces adjacent to the appropriate members in the sketch below. Use the
convention +vc for tension and —\'e for compression. 7 (b) ll'all members ofthe tmss are made from the same hollmv structural section. namely HSS mks l52 x 152 x 4.8. using a steel with a yield stress M350 MPa are the truss members safe
under the 300 lzN load'.1 At what value of load atjoint F. will the truss be on the boundary
between safe and unsach 8 (c) Calculate the deﬂection ofjoint E due to the 300 SN load. Page 3 OHS H H Page J of 8 U H H 4 D H l0
mks The Wolt) 7 24] wide ﬂange rolled steel beam shewn below is continuous over two 12 m spans
and Supports a uniformly distributed load. which includes the beam‘s selfweight. of 50 lthm
The total downwards load of1200 RN is resisted by the three rigid supports at A. B and C. To find
out how much ofthe load is resisted by support B we must consider deformations (:3) Calculate how far down point B would move if‘the support at B was removed. That is ﬁnd
the midspan deﬂection ofa 24 in span beam supported at A and C due to the downward load
ofSO kN/m. Assume E t” 200000 MP3. {b} Calculate how far upjoint B would move due to a 600 lth' point IOad applied at P. That is.
ﬁnd the midspan deﬂection ofa 24 m span beam supported at A and C due to an upwards
point load M600 kN applied at midspan. (cl The actual deﬂection of point B is zero. Hence. the downwards deﬂection due to the 5.0 klﬁfm
load must equal the upwards deﬂection due to the value ofthe support force at B. ls the
support force at B equal to 600 kN'.’ lfnot. what is the correct salue ofthe support force at B',‘ {d} Draw the shear force and bending moment diagrams for the two span beam. Calculate the
highest tensile stress in the steel beam. 350 iaij Page 5 of8 U H U Page 6 of8 H II '1. N mks H H Display your understanding tifstructures and materials lay making brief. insightful comments.
illustrated where appropriate by calculations, on the following topics. issues. quotations or qucsﬁons
(3) Shown below are the stressstrain curves of four different materials. Based on these curves rank materials A. Bl C and D on the basis of strength. stiffness, resilience and toughness.
‘ l l Weakest Flexible i Strangest t
_ Stiffest ' Least Resilien l
""""T——"——' l r" i
t Most Resilient i
l I l l Most Brittl Toughest t 5 (hi To illustrate the concept ofhending a professcir r: W“
mkS uses at wooden metre stick 5. mm thick. lithe i
wood fails at 80 Ml’a and E equals IQOOO Ml’a,
what is the smallest radius of the circular are D into which the stick can be bent just prior to M R M
failure?
b tel “lirmitas. utilitas. venustas“ 5
mks 5 (d) "The Firth ol‘l‘orth Bridge is the clumsicst structures ever designed by man an American till£8 would have taken that bridge with the amount of money that was appropriated and would have turned back 50% to the Owners."
5, {e} The buckling load 0ft! long‘ thin plate With hinged edges (held against displacement} is
t
4T‘E
I1, = ——‘ , bi
l2lb .1 r)” mks For an aircraft structure a 3 m long and l m wide. thin plate with hinged edges is required to safely transmit a compressive force of IOO LN. What is the minimum safe thickness for an
aluminium plate? What is the minimum safe thickness fer a spruce plate”:I Which plate ueighs less? Page 7 MR { r H H . Page 8 of?! ...
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 Winter '08
 Collins
 Force, Truss, mks, Compressive stress, Tensile stress, minimum safe thickness

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