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 = ____________