ENGR0135 - Statics and Mechanics of Materials 1 (2161)Homework #4

Due: 10/7 (daytime sections) or 10/12 (evening section)

1. The assembly shown below consists of a steel (Es = 200 GPa and As = 1400 mm2)tube AB and a brass (Eb = 100 GPa and Ab = 2100 mm2) tube BC. The supports atA and C and the plate at B used to apply the 400 kN load are rigid. Prior to the loadbeing 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

2. The assembly shown below consists of a steel (Es = 200 GPa and As = 1400 mm2) tubeAB and a brass (Eb = 100 GPa and Ab = 2100 mm2) tube BC. The supports at A andC are rigid. The rigid plate at B, that is used to apply the 400 kN load, is securelyfastened to tube AB. Prior to the load being applied, there is a 0.2 mm gap betweenthe rigid plate at B and the brass tube BC. 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

0.2mm

3. A 1/2-in-diameter high-strength steel bolt (Es = 30, 000 ksi) passes through a brasssleeve (Eb = 15, 000 ksi), as shown below. The cross-sectional area of the sleeve is0.344 in2. Determine the normal stresses generated in the bolt and sleeve by tighteningthe nut 1/4 turn (0.020 in).

6 in

5.75 in

rigid washerrigid washer

4. A 50-mm-diameter × 2-m-long aluminum alloy bar (E = 73 GPa and α = 22.5 ×10−6/◦C) is stress-free after being attached to rigid supports, as shown below. Deter-mine the change in temperature required to generate a tensile normal stress in the barof 100 MPa.

2m

5. A 1/2-in-diameter high-strength steel bolt (Es = 30, 000 ksi and αs = 6.6 × 10−6/◦F)passes through a brass sleeve (Eb = 15, 000 ksi, Ab = 0.344 in2, and αb = 9.8×10−6/◦F),as shown below. After the unit is assembled at 80◦F, the temperature is increased to150◦F. If the unit is stress-free at 80◦F, determine the normal stresses in the bolt andsleeve at 150◦F.

6 in

5.75 in

rigid washerrigid washer

6. A short column made of structural steel is used to support the floor beams of a building,as shown below. Each floor beam (A and B) transmits a force of 50 kip to the column.The factor of safety based on failure by yielding is 2.5. Select the lightest wide-flangebeam (see Appendix A-1) that will support the given loads.

A B

50 kip 50 kip

W section