(1) Use beam bending theory to calculate the maximum normal stress in the 25mm diameter, 500mm length aluminum alloy rod at 10mm, 250mm, and 375mm. A transverse force of 50N is applied at the right end as the figure shows. (2) Calculate the displacement at the end of the rod using beam bending theory. (3) Calculate the frequency of the first transverse mode of vibration 50N

(1) Use beam bending theory to calculate the maximum normal stress in the 25mm diameter, 500mm length aluminum alloy rod at 10mm, 250mm, and 375mm. A transverse force of 50N is applied at the right end as the figure shows. (2) Calculate the displacement at the end of the rod using beam bending theory. (3) Calculate the frequency of the first transverse mode of vibration 50N

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter2: Axially Loaded Members

Section: Chapter Questions

Problem 2.3.19P: Repeat Problem 2.3-18, but assume that the bar is made of copper alloy. Calculate the displacements...

See similar textbooks

Similar questions

Solve the preceding problem for the following data: diameter LO m, thickness 48 mm, pressure 22 MPa, modulus 210 GPa. and Poisson's ratio 0.29
A tubular shaft being designed for use on a construction site must transmit 120 kW at 1,75 Hz, The inside diameter of the shaft is to be one-half of the outside diameter. If the allowable shear stress in the shaft is 45 MPa, what is the minimum required outside diameter d?
Compare the angle of twist 1 for a thin-walled circular tube (see figure) calculated from the approximate theory for thin-walled bars with the angle of twist 2 calculated from the exact theory of torsion for circular bars, Express the ratio 12terms of the non-dimensional ratio ß = r/t. Calculate the ratio of angles of twist for ß = 5, 10, and 20. What conclusion about the accuracy of the approximate theory do you draw from these results?
Repeat Problem 2.3-18, but assume that the bar is made of copper alloy. Calculate the displacements SBand Scif P = 50 kips, L = 5 ft = 3/5 in., b1= 2.75 in., b2= 3 in., and E = 16,000 ksi.
A solid cantilevered aluminum alloy rod, 10-mm in diameter, supports a Parol (Christmas Lantern). The hanging Parol subjects the rod to a bending moment of 10.2 Nm along the x-axis, as well as Torque (T) at its fixed end (Section B). If the yield strength oYield in tension of the aluminum alloy is 103.9 MPa at point n of Section B, what is the maximum torque the rod can carry under the maximum distortion-energy theory (MDET)? L aluminum rod Figure 1A Y B cross-section of the rod Figure 1B Image is from Parol clipart 2 Clipart Station
The displacement in x at node 2 is -0.536 mm. If the applied force is increased to -400N, what will the new displacement be? Present your working clearly F = -200N 2 EA/L 45° EA/L y 1 S
Figure 1 shows a composite shaft ABCD acted upon horizontal forces. The moduli of elasticity and the cross-section areas of the segments of the shaft are also provided. Eal = 70 GPa AAB = 58 mm2 Ecu = 126 GPa Est AcD = 39 mm2 = 200 GPa ABC = 77 mm2 %3D %3D Copper 20kN 8 kN Aluminum Steel 7 kN A B 20kN D 8 kN 450 mm 300 mm - 400 mm Figure 1: Axially loaded composite shaft 2.1. Construct the diagram of internal normal forces for each cross-section of the shaft (6) 2.2. Calculate the displacement of the point C with respect to the fixed-point A. (3) 2.3. If the shaft must have one uniform diameter, determine the required minimum diameter of the shaft if the normal yield stress in the composite shaft must not exceed 450 MPa with a factor of safety equal to 1.8. (11)
A solid steel shaft, 90 mm in diameter is coupled in series to a hollow shaft withan external diameter of 100 mm and internal diameter of 90 mm. Calculate thetorsional stiffness of 1 mm length of each of these shafts if they are usedseparately and compare this with the torsional stiffness of a 1 m length of thecompound shaft consisting of a 0.5 m length of each of the shafts mentionedabove. (G = 80 GPa)
Calculate the reaction forces on the bearing near the pulley and bearing at the far end of the shaft. Include a free body diagram and coordinates. Given the shaft length is 1 meter= Mass=40Kg Static load = 8600N Dynamic (running load) = 8400N Some hints:1. This solution will require you to draw known forces and find unknown reactions in 2perpendicular planes and then add the horizontal and vertical reaction forces asvectors to find the reaction force (hypotenuse).2. Bearings are usually mounted as near as possible to the ends of the shaft withoutfouling the other machine elements. The bearing at the far shaft end can be mountedat the 1 meter point. The bearing at the pulley end should allow clearance to assemblethe pulley.3. Bearing reaction forces are typically simplified as a single point load through thebearing centre.
A simple torsion-bar spring is shown. The shear stress in the steel [G = 11,500 ksi] shaft is not to exceed 10000 psi, and the vertical deflection of joint D is not to exceed 0.650 in. when a load of P = 4500 lb is applied. Neglect the bending of the shaft and assume that the bearing at Callows the shaft to rotate freely. Determine the minimum diameter required for the shaft. Use dimensions of a = 84 in., b = 36 in., and c = 34 in. Answer: d= i a D P B in. b C
(Q6) A solid spring steel shaft in small engine with 5hp at 3000rpm is used as a torque measuring device at the rated load. Select a suitable length and diameter combination for this measurement assuming an angular deflection of 10.. The modulus of elastic of the spring steel 28.6x106 psi and the Poisson's ratio is 0.3.
A cold drawn steel rod of circular cross-section is subjected to a variable bending moment of 565 Nm to 1130 N-m as the axial load varies from 4500 N to 13 500 N. The maximum bending momentoccurs at the same instant that the axial load is maximum. Determine the required diameter of the rodfor a factor of safety 2. Neglect any stress concentration and column effect. Assume the followingvalues:Ultimate strength = 550 MPaYield strength = 470 MPaSize factor = 0.85Surface finish factor = 0.89Correction factors = 1.0 for bending= 0.7 for axial load