Exam 2 Solutions

# Exam 2 Solutions - CEN 302 — Mechanics of Materials...

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Unformatted text preview: CEN 302 — Mechanics of Materials Section Exam #2-A SOLuTloms Name ................................................................................................. .. Problem 1. 130 points! The concrete post in Figure (a) is reinforced axially with four symmetrically placed bars, each with a cross sectional area of lSOOmmZ. The moduli of elasticity are 15 0GPa for steel and 15 GPa for concrete. (a) Compute the stress in each material when thg‘l 000 kN load is applied. (10 points), (b) If the initial length of the column is L = 10 5, how much does the column shorten when the load is applied? (5 points) (0) If the allowable stress in the post is lOOMPa for steel and 4MPa for concrete, compute the maximum safe axial load P that may be applied. (5 points) Cw ode (d) If instead of using steel and concrete we only used concrete determine the stress inﬁand the ﬁnal length of the column (after the application of the load).(5 points) (6) What are the longitudinal and lateral strains in this case? What are the new cross-sectional dimensions (average value)? Assume that the Poisson’s Ratio is v = —0.33. (5 points) Eﬁﬁr‘ing piﬁléjhw‘a. I , as SCORBC : 79 Aw“ Ecﬂﬁ3 (Page? 93% ’5 lQGQ ZD m, rm WNW“ , ‘5wa t. gamer: Seating: (2er Week yo v i _W , {5) 0K ’ 6,000x/529 (a) 50W ’ £1”, — ‘fx/ Pat 3 Av , / (Emu Z” “’0” 585,3 _ W know M Zia/biw- pwial Pcﬂﬁt A”? ’14 C _ Pam; MM.» Pg 3 A‘OOQ‘Ps‘. 5M 5 W 31> :5 300mm >< [— 0.000%?) fag/f x 0.. 0Z3 Mn? 5 X, 56%;ZQW/ M'menxi my '1 ’0 [5322373an m3 m ! a.~1~vmﬂmwm18ﬁmwzmmpm"WKIF ﬁnd“, Problem 2 (35 Points) The box beam shown in the ﬁgure below supports the concentrated loads 8001b and 20001b. Calculate the shear and moment diagrams (10 points each). Compute the maximum tensile and maximum compressive stress due to the bending moment (10 points). Show the stress distribution in the section shown below (5 points). A 8001b C 20001b [V] [M] Section — Draw Stress ‘ Distribution I: W'W” A); l; Problem 3 (20 points) Sketch reasonable shear diagrams for the beam conﬁgurations shown below: (<19 ab” @He \) \ l. Problem 4 (15 points) A) Derive the expressions for the shear force and bending moment for each segment of the beam (1) and (3) (7.5 for each). Express shear and moment functions in terms of X. For segment 1, X should be taken as shown below (starting at the left support), While X in the segment 2 should be taken from the right support. 200 1b /ﬁ 400 lb/ft m. ,Atw...;.....—u——-- ,._..__.....____...v..___ .... ~mww...,-»_..~.._.w.i.ﬁ”n.o ,2 + SMEQQ x - 200 X Mi I 2 ...
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Exam 2 Solutions - CEN 302 — Mechanics of Materials...

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