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Unformatted text preview: CIVL 112 Mechanics of Materials Midterm Exam Solutions Q1 (20 marks): The truss shown in Fig. 1 is made of three steel members with E = 210 GPa, and each member has a cross-sectional area of 500 mm 2 . Find (to nearest 0.1 kN) the largest load P that can be applied vertically downward at C, if the roller support at B cannot be displaced by more than 1.6 mm. Fig. 1 Solution: Determination of reactions: F x = 0 A x = 0 By symmetry A y = B y = P/2 Now consider force equilibrium of joint B (assuming both member forces F BC and F BA pull on B, i.e. tension): F x = 0 - F BC cos60 - F BA = 0 F y = 0 F BC sin60 + B y = 0 F BC = - B y / sin60 = - P/2 / [( S 3)/2] = - P/ S 3 F BA = - F BC cos60 = P/(2 S 3) B &lt; 1.6 mm while B = (loading*L) / EA (F BA )(L AB )/(EA) &lt; 1.6 mm P/(2 S 3) &lt; (1.6 mm)(EA)/ L AB P &lt; (1.6 mm)(EA)(2 S 3) / L AB P &lt; (1.6 x 10-3 m)(210x 10 9 N/m 2 )(500 x 10-6 m 2 )(2 S 3) / 4m = 145492.3 N P &lt; 145.5 kN 1 P C Q2 (20 marks) As shown in Fig. 2, a plug with a diameter of 30 mm resides concentrically inside a rigid sleeve whose diameter is 32 mm. Both the plug and the sleeve are 50 mm tall. The plug is made of a material whose E = 5 MPa and...
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