Engineering Answers

5. Two shafts 30 in. apart, each carrying a four-step pulley, are to be connected by a cross belt. The driving shaft is to turn 180 rpm while the driven shaft is to turn 50, 150, 250, and 600 rpm. The smallest step of the driver is 10 in. in diameter. Find (a) the diameters of all the steps, (b) angle of contact for each pair of pulleys, and (c) belt length. Please explain the solution/answer.

Find the directional derivative of fei ( x y z ) =xy^2+yz^3 at ( 2,1,-1) in the direction of i +2j +2k

P500,000 was deposited at an interest of 6% compounded quarterly. Compute the compound interest after 4 years and 9 months.

Answer: P163,475.37

10. A supercritical power generates steam at 25 Mpa and 560􀔨. The condenser pressure is 7 kpa. Determine the exit quality of steam if it expands through a turbine in this power plant.

Answer:

a. 45.66% c. 56.66%

b. 68.45% d. 74.26%

A solid square rod is cantilevered at one end. The rod is 0.6 m long and supports a completely reversing transverse load at the other end of ±2 kN. The material is AISI 1080 hot-rolled steel. If the rod must support this load for 104 cycles with a factor of safety of 1.5 at 100°C, what dimension should the square cross section have? Neglect any stress concentrations at the support end.

The shaft shown in the figure is machined from AISI 1040 CD steel. The shaft rotates at 1600 rpm and is supported in rolling bearings at A and B. The applied forces are F1 = 2500 lbf and F2 = 1000 lbf. Determine the minimum fatigue factor of safety based on achieving infinite life. If infinite life is not predicted, estimate the number of cycles to failure. Also, check for yielding.

A stepped shaft, as shown in figure made from BS080M50 cold drawn steel is subjected to a completely reversed torque T. Based on infinite life, 90% reliability and a factor of safety of 2.1, find the maximum allowable safe torque T, that can be applied, if d = 8 mm.

The figure shows the free-body diagram of a connecting-link portion having stress concentration at three sections. The dimensions are r = 0.25 in, d = 0.40 in, h = 0.50 in, w1 = 3.50 in, and w2 = 3.0 in. The forces F fluctuate between a tension of 5 kip and a compression of 16 kip. Neglect column action and find the least factor of safety if the material is cold-drawn AISI 1018 steel.

The cold-drawn AISI 1040 steel bar shown in the figure is subjected to a completely reversed axial load fluctuating between 28 kN in compression to 28 kN in tension. Estimate the fatigue factor of safety based on achieving infinite life and the yielding factor of safety. If infinite life is not predicted, estimate the number of cycles to failure.

A completely reversed axial load of 20 kN is applied to a machine finished plate (BS 080M50, HR) as shown in the figure. Determine the size b of the plate for indefinite cycle of operation based on Goodman equation. Consider b = 10d = 10t. Choose safety factor of 1.5 and reliability of 99%.