Problem 1. (7 points) For the beam shown, determine (a) the maximum tensile and compressive bending stresses, (b) the maximum shear stress due to V, and (c) the maximum shear stress in the beam.

A 2-in steel plate and a 1-in cast-iron plate are compressed with one bolt, one ½ N American Standard plain washer under the head of the bolt, another identical washer under the nut, and one nut. The bolt is ½ in – 13UNC. Determine: (a)a suitable length for the bolt, rounded up to the nearest 4 in; (b) the bolt stiffness; (c) the stiffness of the members.

Three solid cylindrical rods are welded together to form the compound axial member shown in the figure. The compound axial member is attached to a fixed support at A. Each rod has an elastic modulus of E = 47 GPa. Use the following values for the rod lengths and areas: L = 1530 mm, L2 = 1720 mm, L3 = 1210 mm, A1 = 250 mm^2, A2 = 155 mm, and Az = 65 mm. What magnitude of external load P is needed to displace end Da distance of up= 80 mm to the right? Find the relationship between &1, the elongation of rod (1), and the internal tensile force, F1, in rod (1). Assume &1 is a positive value in units of mm and F1 is a positive value in units of kN. So, the answer you enter for the ratio (&1/F1) must be in units of (mm/kN). Similar to the previous step, find the relationship between 82, the elongation of rod (2), and the internal tensile force, F2, in rod(2). Assume &z is a positive value in units of mm and F2 is a positive value in units of kN. So, the answer you enter for the ratio (&z/F2) must be in units of (mm/kN). Similar to the previous step, find the relationship between 83, the elongation of rod (2), and the internal tensile force, F3, in rod(2). Assume &z is a positive value in units of mm and F3 is a positive value in units of kN. So, the answer you enter for the ratio (&z/F3) must be in units of (mm/kN). Choose the correct relationship between the internal tensile forces in rods (1). (2), and (3), denoted F1,F2, and F3, respectively,and the applied load, P. What magnitude of external load P is needed to displace end Da distance of uD = 80 mm to the right? F_{1}=F_{2}=F_{3}=P \frac{F_{1} L_{1}}{A_{1} E}+\frac{F_{2} L_{2}}{A_{2} E}+\frac{F_{3} L_{3}}{A_{3} E}=\frac{P\left(L_{1}+L_{2}+L_{3}\right)}{\left(A_{1}+A_{2}+A_{3}\right) E} F_{1}+F_{2}+F_{3}=3 P F_{1}+F_{2}+F_{3}=P

14.30D Figure P14.30D shows a cantilevered chain idler sprocket driven by a roller chain that applies a 1200-lb force. Select identical 200 series ball bearings for A and B. The shaft rotates at 350 rpm. 14.31DRepeat Problem 14.30D, except the shaft rotates at 275 rpm.

A helical compression spring is to be made with a wire diameter of 2 mm, an out-side diameter of 19 mm, ten active coils, and ends closed and ground. The least expensive steel spring wire is to be used, and presetting will not be used. (a) Estimate the maximum static load that can be applied without encountering more than 2 percent long-term set. (b) What is the spring rate? (c) At what spring free length will the load determined in part (a) cause the spring to become solid? (d) Would buckling problems be encountered if one end plate is free to tilt? Repeat Problem 12.25, except use a wire diameter of 4 mm and eight active coils.

For the bearing application specifications given in Table A, determine the Basic Load Rating for a ball bearing with which to enter a bearing catalog of manufacturer 2 in Table 11-6. Assume an application factor of one.

The offset slider-crank mechanism shown is operating with a constant input speed and an average backward speed of 30 cm/s. Determine dead-center positions, stroke, time ratio, average forward speed, range of oscillating angle of the connecting rod and satisfaction of this range. Use given plot to verify the theoretical calculations. Also determine the minimum suitable length of the connecting rod for which o is in the appropriate range, and how does the oscillating range change according to that length. Adjust the mechanism's offset such that the time ratio becomes 0.8.

Two parts of a machine are held together by bolts that are initially tightened to provide a total initial clamping force of 10,000 N. The elasticities are such that kc = 2kp. (a) What external separating force would cause the clamping force to be reduced to1000 N (assume that the bolt remains within its elastic range)? (b) If this separating force is repeatedly applied and removed, what are the values of the mean and alternating forces acting on the bolts?

In the figure shown, shaft OA, made of AISI 1030 hot-rolled steel, is welded to a fix support at 0 and subjected to loading by forces F1, F2, F, and the external moment Me as shown below. The shaft has a20 mm. Any possible deformation of the shaft will take place along the x-axis only, and diameter d axial stresses are neglected. Stresses are to be considered at support O. The forces are F120 N, F230 N, and F350 N, and Me= 10 N.m. 1. Find the moment(s) and torque(s) that each force will produce on the shaft at O [4.5 Marks] 2. Find the resultant moment and resultant torque at O [4 Marks 3. Find the bending and shear stresses at O [3 Marks] 4. Find the factor of safety for shaft OA by using the Maximum Shear Stress theory and specify whether the structure is safe or not 3.5 Marks]

A transmission shaft supporting a spur gears B and the pulley D is shown in the Figure below. The shaft is mounted on two bearings A and C. The diameter of the pulley and the pitch circle diameter of the gear are 450 mm and 300 mm respectively. The pulley transmits 20 kW power at 500 rpm to the gear. P₁ and P₂ are belt tensions in the tight and loose sides, while P₁ and P, are tangential and radial components of gear tooth force. Assume, P₁= 3P₂ and P, = P, tan (20°). The gear and pulley are keyed to the shaft. The material of the shaft is steel AISI 1144 OQT 1000. Determine the shaft diameter on strength basis. Use K₁ = 1.5 and design factor of 4. Design for reliability of 0.99 and you may assume size factor of 0.75 for the start. In doing so, follow the following steps: (a) Compute the torque delivered to the shaft at B. (b) Compute the belt tensions P₁ and P₂ at pulley D. (c) Compute the reactions at the bearings A and C. (d) Draw the complete free-body diagrams and bending moment diagrams of the shaft in horizontal and vertical planes (e) Determine the modified endurance strength of the shaft. (f) Determine the minimum acceptable diameter of the shaft.