A rigid block (neglect its weight) is to be supported by three equally spaced rods (spaced by a distance a), each of which has Young's modulus E, cross section area A and length L. The rods are to be pinned to the block, but during assembly it is found that one of the bars is slightly too long; before it is attached its pin-hole extends a small distance s beneath the corresponding hole in the block. To finish the assembly, the ʻover-sized bar' is compressed and attached to the block, and then the assembly is released. (1) Find the force that is induced in each of the three bars in terms of parameters E, A, L, s and a (note that you may not need all of them). (2) After the assembly, we increase the temperature of the first and the third rod (temperature of the second rod is kept the same). The thermal expansion coefficient is a. Is it possible to achieve zero forces in the first and third rod (F1 = F3 = 0) during the heating process? If yes, find the required temperature increase AT, in terms of E, A, L, s, a and a (note that you may not need all of them). If no, explain the reason.

A rigid block (neglect its weight) is to be supported by three equally spaced rods (spaced by a distance a), each of which has Young's modulus E, cross section area A and length L. The rods are to be pinned to the block, but during assembly it is found that one of the bars is slightly too long; before it is attached its pin-hole extends a small distance s beneath the corresponding hole in the block. To finish the assembly, the ʻover-sized bar' is compressed and attached to the block, and then the assembly is released. (1) Find the force that is induced in each of the three bars in terms of parameters E, A, L, s and a (note that you may not need all of them). (2) After the assembly, we increase the temperature of the first and the third rod (temperature of the second rod is kept the same). The thermal expansion coefficient is a. Is it possible to achieve zero forces in the first and third rod (F1 = F3 = 0) during the heating process? If yes, find the required temperature increase AT, in terms of E, A, L, s, a and a (note that you may not need all of them). If no, explain the reason.

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter6: Beams And Cables

Section: Chapter Questions

Problem 6.63P: The cable of the suspension bridge spans L=140m with a sag H=20m. The cable supports a uniformly...

See similar textbooks

Similar questions

Design a knuckle joint subjected to axial tensile forceof 50 kN. Determine the dimensions for the knucklejoint whose rods and pin are made from a selectedmaterial, Steel-Cast (Syt=500MPa) withfactor of safety of 3 .
The fabricated steel members are being assembled into a truss on-site in the municipality of Alfonso, Cavite. The assembly started at the elevated ground at both sides and is to meet at the midspan. Nearing to the end of construction, it was found that the last member, CD, was fabricated too short by A D= 4.450 mm. The engineer then came up with an idea of applying a force P at joints C and D as shown to close the gap. P. с c' P 3 m -3 m- -3 m- 3 m- Use E = 200 GPa and cross-sectional area of members BC, DE, CD each 4500 mm2 while AC and DF being 6363.961 mm2 a) Determine the necessary force, P, to close the gap in kN. wwww b) If force P will then be removed after being assembled, calculate the force in CD in kN.
Draw the free-body diagram for the following problem. The rod shown.
Situation 3: Four plates, 10 mm thick each, are connected by 25-mm diameter rivets as shown. Assume that the force will be equally distributed among the rivets. Take note that each hole diameter is 3 mm wider than the rivet diameter. A. How much punching force is required to create a hole in a single plate? Round your answer by 5 kN. B. What is the maximum allowable force P that can be applied on the middle P 100 mm plates considering the given allowable stresses? (kN) C. If P = 10 kN, what is the normal stress Allowable stresses: Bearing stress of each plate: 20 MPa Shearing stress of each rivet: 15 MPa Shearing stress of each plate: 12 MPa of the top plate at section a-a? (MPa)
The cable of the suspension bridge spans L=140m with a sag H=20m. The cable supports a uniformly distributed load of w0 N/m along the horizontal. If the maximum allowable force in the cable is 4 MN, determine the largest permissible value of w0.
Problem # 20. fowe for the reacilon forces if a 40-kN force ķ appeied on the steel rod, near and tow ards the connection. Given: ateel rod alloy aluminum alloy 40 Cm 30 Cm A 40 cm Ateel rod alloy has -em diameter wherein diameler long a 30-em long alliminum alloy with D.5 cnm A connected on ts end . Young a modulua of steel = 200 6Pa toungai moaulna of aluminum = I20 6Pa The poda are attiached to gether and both" are Constrainedu sidea
Force P is applied as shown on the 13.5 mm thick plate. P = 100 kN. Holes are oversized causing all rivets to always proportionately react to load applied on the plate. 1. Which of the following most nearly gives the force in rivets if P is applied at the centroid of four(rivets)? a. 50 kN b. 30 kN c. 25 kN d. 40 kN 2. Which of the following most nearly gives the force in rivets if only moment equals P times e is applied at the centroid of four(rivets)? a. 12.567 kN b. 10.451 kN c. 32.672 kN d. 17.678 kN 3. Which of the following most nearly gives the maximum force in rivets due to combined effect of P and torque? a. 42.28 kN b. 40.93 kN c. 39.53 kN d. 37.34 kN 4. Considering shearing in bolts, what is the minimum required diameter if allowable shearing stress in bolts is Fv/2, Fv = 372 MPa a. 27.34 mm b. 14.53 mm c. 16.45 mm…
Solve the truss structure using the joint's method, when m = 100 kg.
A 280-kg uniform rectangular plate is supported in the position shown in the figure by hinges A and Band by a cable DCE that passes over a frictioniess hook at C. Assume that the tenslon is the same in both parts of the cable and that hinge B does not exert any axial thrust. 060mm etcok 150 zim Print 90mm 675 mmm eferences 270 m Problem 04.117.c - Reactlon from plate Determine the reactions at Aand B INT- N k. The resction at As the reserion at 5s 1573 N)
In the assembly shown, sags of s and 1.5 s resultedwhen the two cylinders were suspended from the rings at A and B, respectively. If s =0 when the cylinders are removed, determine the fallowing: a. the horizontal distancex (mm) moved by point B b. the mass (kg) of thetwo cylinders c. the forces (N) in the two springs d. thetension (N) in cable AB e. the spring constant kag - 2 m +1m- - 2 m www 1.5 m 1.5s Note: Use9.81m/s2for thegravitational constant and kgn=134 N/m. X = 7, Y = 3, Z = 7 S =0.8+0.0003*737% = 1.0211 m Parameter S =0.8+0.0003*XYZ m
1. Determine the pin reactions at 'A'. B -30 lb 20" D 50 lb 20" E 12 C -30"-
3 Please help. Provide Free Body Diagram, labeled with appropriate quantities to better understand. Also solve. Thank you.