ENGR246Mechanics of Materialsinstructor

Assignment 2Perfect Score: 100 pts

Due: 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 75 x 35 x 25 mm. When subjected to force P = 10 kN the ‘b’ dimension changes to 35.00250 mm. If Poisson’s ratio  = 0.35, determine (a) the modulus of elasticity, E and (b) the loaded L dimension to 5 decimal places.

a) E = 56.00b) LLoaded= 74.98469

☺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=10,100,000psi, EST=29,000,000psi)

Minimum diameter 1.22 Control: ??

Problem 3 (10 pts)

Link CE (aluminum EAL=10.4 x 106 psi) has a cross-sectional area of 0.500 in2. Link BD (brass EBR=15 x 106 psi) has a cross-sectional area of 0.400 in2. Determine the force P that can be applied at A if the deflection of A is not to exceed 0.0140 in.

PMAX = 3.513

Problem 4 (10 pts)

The “rigid” beam AD is supported by a pinned connection at A and by two steel rods having1/16 inch diameter and modulus of elasticity E=29 x 106 psi. The rods were taut before applying the load at P. If the deflection of point D is 0.06907 inch, what is the applied load at D?

PD = 220

Problem 5 (10 pts)

The concrete post is reinforced with6 22mm diameter steel bars. A temperature change induces a change in stress of 9.475MPa in the steel bars. Determine the temperature change and the change in stress in the concrete. Square post cross-section measures 240mm x 240mm. EST= 200GPa ECON = 25GPa; ST=11.70 mm/mm/°C, CON=9.90 mm/mm/°C

T = 35.00CONCRETE = 0.391

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 = 1.000 kN without exceeding the allowable shear stress of 5 MPa and shall have a spring constant k = 100N/mm. If the modulus of rigidity is 50 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 = 240.000a = 100.00b) MAX = 10.00

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 10.00000 mm. x 25.00000 mm x 50.00000 mm. After loading with forces acting through the centroid the size changed to 10.00055 in. x 24.98875 mm. x 49.92750 mm. Determine the forces acting on the solid. Assume  = 0.28 and E = 200 GPa.

a) FX = -102,503.6b) FY = -218,572.4c) FZ =-126,882.1

Problem 8 (20 pts)

The following load vs. elongation data was obtained for a (fictitious) metallic tensile specimen with a square cross-section measuring 12 mm x 12 mm. The extensometer gage length was 25 mm. Using engineering stress and strain, determine themodulus of elasticity, yield strength, ultimate strength, per cent elongation at failure, modulus of resilience and the modulus of toughness.

Load N / L mm / Load N / L mm / Load N / L mm / Load N / L mm
0 / 0 / 17280.0 / 0.015000 / 30960.0 / 0.500000 / 28317.6 / 2.500000
4320.0 / 0.003750 / 21600.0 / 0.018750 / 33120.0 / 1.000000 / *** / ***
8640.0 / 0.007500 / 25920.0 / 0.022500 / 33120.0 / 1.500000 / *** / ***
12960.0 / 0.011250 / 28800.0 / 0.025000 / 31464.0 / 2.000000 / *** / ***

E = 200Y = 200ULT = 230.00

%elong = 10UR = 100.0UT = 21,729.0

☺Problem 9 (10 pts)

The concentric axial load P applied to the bar shown is 41,528 N. Determine the magnitude and location of the peak stress (at hole A? or hole B?).

PEAK= 120Location: ??

♦Problem 10 (10 pts)

Consider the tapered rod. When measured at room temperature TO= 20°C, the length L = 1 m, diameters d1= 11.1mm and d2= 5.5 mm. Due to variations in thermal insulation, the rod temperature is observed later to vary linearly along its length from 200°C at the end with the larger diameter to 90°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  = 12 x 10-6 mm/mm/°C and E = 200 GPa.

LFREE = 1.5000P = 14384.6MAX =605.5

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