# A tractor is moving slowly over a bridge, as shown in figure given below. The force exerted on the bridge by the tractor are 4050 lb by the rear wheels and 1010 lb by the front wheels. Determine the position x of the tractor for which the bending moment in the beam is maximum.

A tractor is moving slowly over a bridge, as shown in figure given below. The force exerted on the bridge by the tractor are 4050 lb by the rear wheels and 1010 lb by the front wheels. Determine the position x of the tractor for which the bending moment in the beam is maximum.

NOTE: Maximum three students per group is allowed. Do all the problems. Problems carry different weights. Students are expected to look up information that is not given in the problem statement.
[20 marks] Problem #1: A tractor is moving slowly over a bridge, as shown in figure given below. The force exerted on the bridge by the tractor are 4050 lb by the rear wheels and 1010 lb by the front wheels. Determine the position x of the tractor for which the bending moment in the beam is maximum.

[45 marks] Problem #2: The motor shown in the following figure supplies a torque of 380 lb.ft to shaft BCD. The torques removed at gears C and D are 220 lb.ft and 160 lb.ft, respectively. The shaft BCD has a constant diameter and is made of 0.4% C hot-rolled steel with an allowable shearing stress of 15 ksi. The angle of twist between B and D cannot exceed 3.0o. Each of the segments BC and CD of the shaft has a length of 4 ft. Determine
(a) The minimum permissible diameter of the shaft, if shafts are available with diameters in increments of 1/8 in.
(b) The diameter of the bolts used in the coupling, if eight bolts are used, and the allowable shearing stress for the bolts is 7000 psi. The diameter of the bolt circle is d1 = 3.5 in., and bolts are available with diameters in increments of 1/16 in.

[35 marks] Problem #3: A cold-rolled steel tension bar AB and a structural steel (E = 29,000 ksi, and ?y = 36 ksi) compression strut BC are used to support a load P = 100 kip, as shown in the following figure. Assume that the pins at B and C offer no resistance to bending about the x-axis but provide end conditions which are essentially fixed at C and free at B for bending about the y-axis. Select the lightest structural steel section (use structural Tees) that can be used for strut BC. Use Code 1.
Note: structural tees are not listed in your textbook. It is your responsibility to look up information on this type of beams.

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