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Unformatted text preview: Name: UNIVERSITY OF TORONTO
FACULTY OF APPLIED SCIENCE AND ENGINEERING
FINAL EXAMINATIONS, DECEMBER 2004
First Year ~— Program 5 CIV IOZHIF — STRUCTURES AND MATERIALS Examiner — M.P. Collins Permissible Aids: notebook, calculator and drafting instruments 1. The steel truss shown below supports a bridge Spanning 24 m. When a battalion of soldiers
walks across the bridge, joints C,E, G, l and K are each subjected to a downwards force of 60
kN due to the weight of the soldiers and the self weight of the bridge. 10 (a) Calculate the axial force in each member of the truss due to the ﬁve 60 kN load. List mks your results in the table on page 2. Use the convention +ve for tension and ——ve for
compression.
8 D F H 3' L.
H l
‘ c a q I K M
60W 6!) 1w . 60 (w 60h» 40h:
4. m 4 In 4 m 4 W 444 A M Page 1 of 8 7
mks 1 4
mks (b) The top horizontal members (BD, DF, etc) are HSS 152x 152 x 4.8, the bottom
horizontal members (AC, CE, etc) are HSS 102 x 102 x 6.5, while the diagonal
members (AB, BC, CD, etc) are HSS 102 x 102 x 8.0. Are the truss members safe
under the 60 kN load? At what value of the ﬁve equal point loads will the truss be on the boundary between safe and unsafe? (c) Calculate the midspan deﬂection of the bridge due to the ﬁve 60 RN loads. Use the
method to virtual work. Fill in the table above. What is the natural frequency of the bridge with the soldiers on it? Page 2 of 8 8 (d) The battalion is in a hurry and instead of breaking step and walking it crosses the bridge
mks in a “double time march” which involves 180 steps per minute. This results in the ﬁve
forces applied to the truss varying in a cyclic manner from a minimum of 40 kN to a
maximum of 80 kN. Under this situation what will be the maximum deﬂection of the bridge? Assume a damping value of 0.01. 6 (e) Because of the cyclic marching loads the forces in the members of the truss will be larger mks than the values calculated in part (a). The forces will increase by a factor equal to the
maximum deﬂection calculated in part (d) divided by the deﬂection calculated in part (c).
This increase in the forces will decrease the factor of safety for the truss members. What
will be the smallest factor of safety as the soldiers march across the bridge? Note that a factor of safety less than 1.0 implies that the bridge would fail. Page 3 of 8 2. A designbuild competition challenges your team to build the strongest possible beam to span 7
mks 6
mks 950 mm and carry a point load at midspan, using a 1015 mm X 812 mm x 1.27 mm thick
sheet of cardboard. The cardboard has a tensile strength of 16 MPa, a compressive strength
of 6 MPa, a shear strength of 4 MPa and a modulus of elasticity of 4000 MPa. One member
of your team has suggested the simple design shown below. It consists of a top ﬂange made
by gluing together three pieces of cardboard and two vertical webs each made from one piece
of cardboard. The remaining cardboard is used to make diaphrang at midspan and at the supports. (a) Calculate the location of the centroid and the value of I for the proposed section of the
bridge. (b) Use the. momentarea theorem to calculate the mid~span deﬂection of the beam when the
point load is 200 N. Page 4 of 8 6 (c) Use Navier’s equation for ﬂexural stress to determine the value of P which will cause a
mks tensile stress of 16 MPa at midspan and then determine the value of P which will cause a
compressive stress of 6 MPa at midspan. 4 (d) Use J ourawski’s equation for shear stress to determine the value of P which will cause a
mks shear stress of 4 MPa Page 5 of 8 6 (e) Based on the results in parts (0) and (d) what would be the predicted failure load for the
mks proposed bridge? Will plate buckling reduce this failure load and if so by how much? 6 (f) Suggest how the proposed design can be improved so that the failure load will be
mks increased. Page 6 of 8 20
mks p, .3. Prof. Alexander of Leeds University has observed that for the bones of both birds and
mammals “bending is the predominant form of applied stress”. It is because of this that many bones resemble circular tubes. In mammals the space in the centre of the bone is
usually ﬁlled with fatty yellow marrow. This marrow performs no structural function but
does weigh about 8 kN/m3 and hence increases the weight of the bone, W. Bone breaks at
about 180 MPa and weighs 20 kN/m3. Consider such a bone 300 mm long, supported at each
end and loaded with a point load; P, at midspan. The bone has an external diameter, D0, of
30 mm. Prepare a plot showing how the breaking loadtoweight ratio, P/W, of the bone
beam changes as the ratio Di/D0 changes from 0 to 0.9. Comment on design considerations
for the bone if it is desired to maximize P/W. Page 7 of 8 4. Display your understanding of structures and materials by making brief, insightful
comments, illustrated where appropriate by calculations and diagrams, on the following two structures. a) John Smeaton’s tower for the Eddystone Lighthouse. mks Smeaton’s Tower b) Robert Maillart’s Salginatobel Bridge. mks Salginatobel Bridge Page 8 of 8 ...
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 Winter '08
 Collins
 Force, Strength of materials, Truss, mks, Compressive stress, Tensile stress

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