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Unformatted text preview: McGill University
Faculty of Engineering SOLID MECHANICS
CIVE207A01 Final Examination: 2:00 — 5:00 PM, DECEMBER 8, 2006 Examiner: Prof. Shao Coexaminer: Prof. McClure bFEQ :\ [hat/wk STUDENT NAME: MCGILL ID. NUMBER: INSTRUCTIONS: 1) This is a closed book examination. N0 crib sheet is allowed. 2) Only faculty standard calculators are permitted. _
3) This examination consists of SIX problems of a total of 5 pages, including cover page. 4) The examination will be marked out of 100. CIVE207A Final Examination December 8, 2006 p.2 Problem 1 110 marks): An inﬂatable structure used by a traveling circus has the shape of a halfcircular cylinder with
closed ends (see Fig. 1). The fabric and the plastic structure is inﬂated by a small blower and has
a radius of 40 ft when fully inﬂated. A longitudinal seam runs the entire length of the “ridge” of
the structure. If the seam tears open when it is subjected to a tensile load of 540 pounds per inch of seam, what is the factor of safety (F S.) against tearing when the internal pressure is 0.5 psi and the structure
is fully inﬂated? Longitudinal seam Fig. 1: Problem 2 (15 marks): An elastic prismatic beam with an overhang is loaded with a concentrated end moment Mo and
supported by a spring at B (see Fig. 2). Determine the deﬂection of the free end A. The spring
constant k = 48EI/L3, where E1 is the ﬂexural stiffness of the beam. Express the deﬂection in
terms of M0, L, a, and E1. [Hintz P=kA, where P=spring force, A=spring displacement] CIVE207A Final Examination December 8, 2006 p.3 Problem 3 (15 marks): A thin bar of stainless steel (6mm wide and 3mm thick) is axially precompressed 100 N
between two plates that are ﬁxed at a constant distance of 150 mm apart (see Fig. 3). This
assembly is made at 20 0C. How high can the temperature of the bar rise so as to avoid buckling?
Assume factor of safety = 2, E = 200 GPa and coefﬁcient of thermal expansion or = 15 x 10'6 per
0C. Fig. 3a is a front view and Fig. 3b a side view. Dimension is in mm. (Hint: For column with pinpin ends, L6 = L; for column with ﬁxedﬁxed ends, L6 = 0.5L.) Fig. 3: T
3 1 o
6 i (a) (b) Problem 4: (15 marks! A 4in. by 4in. by 2in. (thick) concrete block is subjected to biaxial compression by force PX
and Py acting through loading pads, as shown in Fig. 4a. (1) Determine the compressive axial
load PX (in kips) if the vertical force is Py = 8 kips and compressive normal stress on the x’ and y’
planes have the value shown in Fig. 4b. (2) Construct a Mohr’s circle of stress at point A. (3) Use
this Mohr’s circle to determine the shear stress, Ixeyv, on x’ plane. CIVE207A Final Examination December 8, 2006 p.4 Problem 5: [20 marks! A cantilever beam has a cross section shown in Fig. 5 and is loaded at the free end. Knowing that
the vertical force P = 20 kN acts at the left corner of the section, determine the torque T that
would cause the section to twist. All members are to be considered thin walled and calculation should be based on the centerline dimensions. Moment of inertia of the section
I = 13.43 x106 mm4. Problem 6: 125 marks! A horizontal L—shaped rod is connected by a taut wire to a cantilever beam, as shown in Fig. 6. If
a drop in temperature of 100 0C takes place in wire and a downward force P = 250 N is applied at
the end of the cantilever beam, determine the maximum normal stress and maximum shear
stress occurred in the structure. Assume the wire carries no stress before the temperature is
dropped and the load is applied. All dimensions shown in the ﬁgure are in mm. The diameter of
the bent rod, as well as that of the cantilever beam, is 20 mm. The cross sectional area of the wire
is 0.4 m2. The assembly is made from steel having E = 200 GPa, G = 80 GPa and coefﬁcient of
thermal expansion (1 = 11.7 x 10'6 per 0C. [Hint tan20p=2IXy/(oxoy)] CIVE207A Final Examination December 8, 2006 p.5 Useful formulas for section properties: Appendix D. Beam Deflections and Slopes _ Maximum I
Beam and Loading Elastic Curve Deflection Slope at End Equation of Elastic Curve _ PP PLZ p 3
3E] _2_EI y = Ea — 3Lx2)
WL4 wL3 = — w ( 4 — 4Lx3 2
SE] 6E1 y 24E] x + 6L x2) ...
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 Winter '09
 Shao

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