ENGR246 Mechanics of Materials Assignment 2 Due: Ionashku_A Perfect Score: 100 pts January 28, 2010 at start of class. Late work receives NO CREDIT Instructions: Solve ALL problems below. Enter correct answers with correct units in the space provided on this Cover Sheet. Express all results with a minimum of 3 significant figures. Attach supporting handwritten work to this Cover Sheet. NO WORK = NO CREDIT. Supporting handwritten work shall CLEARLY indicate your name, chapter and problem number. See syllabus for additional information related to scoring rubric. ☺Problem 1 (10 pts) The ‘unloaded’ dimensions (L x b x h) of solid block of isotropic material shown are 150 x 70 x 50 mm. When subjected to force P = 145.5 kN the ‘b’ dimension changes to 70.01551 mm. If Poisson’s ratio = 0.24, determine (a) the modulus of elasticity, E and (b) the loaded L dimension to 5 decimal places. a) E = ___________ b) LLoaded= _________ 65 kip ☺Problem 2 (10 pts) The “stepped” aluminum rod ABC shown is to be replaced with a solid steel rod of the same overall height. The vertical deflection of the steel rod shall not exceed that of the aluminum rod under the same load and the allowable stress in the steel rod shall not to exceed 24 ksi. Determine the minimum diameter of the replacement rod. What controls this design decision, strength or deflection? (EAL=10,100,000 psi, EST=29,000,000 psi) Min. diameter: ________ 18in 39in 2in 4.30in Control: ____________ Problem 3 (10 pts) Link CE (aluminum EAL=10.4 x 106 psi) has a cross-sectional area of 0.600 in2. Link BD (brass EBR=15 x 106 psi) has a cross-sectional area of 0.300 in2. Determine the force P that can be applied at A if the deflection of A is not to exceed 0.0380 in. 5.5in 12in PMAX = ____________ 8 in 4in Problem 4 (10 pts) The “rigid” beam AD is supported by a pinned connection at A and by two steel rods having 7/16 inch diameter and modulus of elasticity E=60 x 106 psi. The rods were taut before applying the load at P. If the deflection of point D is 0.01262 inch, what is the applied load at D? PD = ______________ 2in 16in Problem 5 (10 pts) The concrete post is reinforced with 4 12 mm diameter steel bars. A temperature change induces a change in stress of 12.935 MPa in the steel bars. Determine the temperature change and the change in stress in the concrete. Square post cross-section measures 180 mm x 180 mm. EST= 200 GPa ECON = 25 GPa; ST=11.70 mm/mm/°C, CON= 9.90 mm/mm/°C T = ____________ CONCRETE = _____________ Problem 6 (10 pts) A vibration isolator is to be made from two square elastomer blocks measuring s x s x a bonded to rigid plates as shown. The isolator shall support a maximum load PMAX = 1.150 kN without exceeding the allowable shear stress of 9 MPa and shall have a spring constant k = 67N/mm. If the modulus of rigidity is 32 MPa, determine (a) the smallest size block and (b) it’s deflection under maximum load. Assume small displacement such that = a tan() ~ a. a) s = ________ b) MAX = ________ a = ________ Is the small displacement assumption appropriate? _____ Why or Why not? ________________________ ♦Problem 7 (10 pts) The size (h x w x L) of a rectangular solid before loading is 12.00000 mm. x 24.00000 mm x 135.00000 mm. After loading with forces acting through the centroid the size changed to 12.00516 in. x 23.99820 mm. x 134.76375 mm. Determine the forces acting on the solid. Assume = 0.32 and E = 230 GPa. a) FX = ___________ b) FY =___________ c) FZ = __________ Problem 8 (20 pts) The following load vs. elongation data was obtained for a (fictitious) metallic tensile specimen with a square cross-section measuring 20 mm x 20 mm. The extensometer gage length was 50 mm. Using engineering stress and strain, determine the modulus of elasticity, yield strength, ultimate strength, per cent elongation at failure, modulus of resilience and the modulus of toughness. Load N 0 7380.0 14760.0 22140.0 L mm 0 0.007500 0.015000 0.022500 Load N 29520.0 36900.0 44280.0 49200.0 L mm 0.030000 0.037500 0.045000 0.050000 Load N 52890.0 56580.0 56580.0 53751.0 L mm 0.775000 1.550000 2.325000 3.100000 Load N 48375.9 *** *** *** E = __________ Y = ___________ ULT = ___________ %elong = _________ UR = ___________ UT = ___________ ☺Problem 9 (10 pts) The concentric axial load P applied to the bar shown is 54,861 N. Determine the magnitude and location of the peak stress. PEAK =___________ Location: __________ P = __________ 58 mm 18 mm 130 mm ♦Problem 10 (10 pts) Consider the tapered rod. When measured at room temperature T O= 22°C, the length L = 3.75 m, diameters d1= 13 mm and d2= 4 mm. Due to variations in thermal insulation, the rod temperature is observed later to vary linearly along its length from 170°C at the end with the larger diameter to 40°C at the end with the smaller diameter. Determine the rod’s FREE thermal expansion L. Determine the axial load P required to reduce the free expansion to ZERO and the resulting maximum stress Assume = 19 x 10-6 mm/mm/°C and E = 150 GPa. LFREE = __________ L mm 3.875000 *** *** *** MAX = ____________

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