ENGR0145 - Statics and Mechanics of Materials 2 (2131) Homework #1 Due: September 5, 2012 1. A 500 kg mass is supported by steel cables A and B, as shown below. Determine the minimum diameters required for the two cables if the allowable normal stress in the cables is 150 MPa. A B 45 ◦ 500 kg 2. A system of three steel pipes, AB, BC , and CD, is loaded and supported as shown below. The loads are applied to the rigid plates that connect the pipes at B, C , and D. If the normal stress in each pipe must not exceed 24 ksi, determine the minimum cross-sectional areas required for each of the pipe sections. 14 in 16 in 20 in A B C D 30 kip 5 kip 15 kip 3. A 0.75 in diameter solid aluminum rod is press fit into an aluminum pipe, whose inner diameter is 0.75 in and outer diameter is 1 in, as shown below. Determine the average shearing stress at the interface between the rod and pipe, if the depth of the press fit L is 0.75 in and the applied axial load P is 100 lb. P P L
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ENGR0145 - Statics and Mechanics of Materials 2 (2131)Homework #1
Due: September 5, 2012
1. A 500 kg mass is supported by steel cables A and B, as shown below. Determine theminimum diameters required for the two cables if the allowable normal stress in thecables is 150 MPa.
A
B
45◦
500 kg
2. A system of three steel pipes, AB, BC, and CD, is loaded and supported as shownbelow. The loads are applied to the rigid plates that connect the pipes at B, C, andD. If the normal stress in each pipe must not exceed 24 ksi, determine the minimumcross-sectional areas required for each of the pipe sections.
14 in 16 in 20 in
A BC
D
30 kip 5 kip 15 kip
3. A 0.75 in diameter solid aluminum rod is press fit into an aluminum pipe, whose innerdiameter is 0.75 in and outer diameter is 1 in, as shown below. Determine the averageshearing stress at the interface between the rod and pipe, if the depth of the press fitL is 0.75 in and the applied axial load P is 100 lb.
PP
L
4. A steel bar, with a rectangular cross section, has a butt-welded joint, as shown below,and will be used to carry an axial tensile load of 750 kN. If the normal and shearstresses on the plane of the weld must be limited to 80 MPa and 50 MPa, respectively,determine the minimum thickness t required for the bar.
60◦ 750 kN750 kN 125mm
5. A system of three steel (E = 30, 000 ksi) pipes is loaded and supported as shownbelow. The loads are applied to the rigid plates that connect the pipes at B, C, andD. Determine the change in length of the complete system of pipes if the cross-sectionalareas of pipes AB, BC, and CD are 1.2 in2, 1.0 in2, and 0.8 in2, respectively.
14 in 16 in 20 in
A BC
D
30 kip 5 kip 15 kip
6. The assembly shown below consists of a steel (ES = 200 GPa and AS = 1500 mm2)tube AB and a brass (EB = 100 GPa and AB = 2000 mm2) tube BC. The supportsat A and C and the plate at B used to apply the 400 kN load are rigid. Prior to theload being applied, the tubes are stress-free. When the load is applied, determine
(a) The normal stresses in each tube.
(b) The deflection of the rigid plate at B.
200 kN
200 kN
A
BC
BrassSteel
1.5m 1m
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