when they are initially pinned to a straight, rigid, horizontal beam BF. Subsequentially, heating of the rods causes them to elongate and leaves the beam in the position denoted by B*D*F*. Point D moves vertically downward by a distance 8p = 0.24 in., and the inclination angle of the beam is 0 = 0.5° in the counterclockwise sense, as indicated on Fig. P2.3-8. Determine the strains e₁, 2, and e, in the three rods. VEXE Jc E O 6 ft (2) (3) B 3 8p -3 ft BL D* P2.3-8 2 ft- F* 4 ft 10

when they are initially pinned to a straight, rigid, horizontal beam BF. Subsequentially, heating of the rods causes them to elongate and leaves the beam in the position denoted by BDF. Point D moves vertically downward by a distance 8p = 0.24 in., and the inclination angle of the beam is 0 = 0.5° in the counterclockwise sense, as indicated on Fig. P2.3-8. Determine the strains e₁, 2, and e, in the three rods. VEXE Jc E O 6 ft (2) (3) B 3 8p -3 ft BL D P2.3-8 2 ft- F* 4 ft 10

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 2.3.21P: A slightly tapered bar AB of solid circular crass section and length L is supported at end B and...

See similar textbooks

Similar questions

Question 4 A composite rod of 160 mm in length, is composed of 50 mm in diameter for a length of 100 mm and 30 mm for the remaining 60 mm. If the Young modulus of the composite is 200 GPa and the application of gradual load P in the rod results in storing 10 J of energy, calaculate: The magnitude of the applied load 4.1 4.2 The value of the stress in each section 4.3 The total extension 4.4 If this load had been applied suddenly but without shock or impact, what instantaneous maximum stress would have been induced in the link?
6) Determine the reactions at A and B for the steel bar and loading shown in Fig. I, assuming a close fit at both supports before the loads are applied. A = 250 mm? 150 mm 30X0 KN 150 mm A = 400 mm2 150 mm K 600 kN 150 mm B 7) A steel bar 20 mm square in section is subjected to an axial compressive load of 60 kN. Find the percentage change in volume if the bar is 500 mm long. What are the equal stresses that must be applied to the sides of the bar if the volumetric change is to be zero? E = 200GPA and v=0.3.
The stresses in a 2-D rectangular steel body (E = 200 GPa, v=0.32) are xx = -A(L - x)y, and oxy = A(h² - 4y²); other stress components are zero. Here, L represents length and h is height. What is the strain component y xy A - (h² - y²) 8E O A A 8G - (h²-x²) - (h²-x²) 8E А A= (h²-y:²) 8G ?
A steel torsion bar AB with diameter d = 34 mm, and ductile material of tensile yield strength Sy = 276 MPa is attached to a rigid arm at A, supported by a bearing at C, and fixed at B, as the picture shows. At the right end of the arm is mounted the wheel on which the vertical force P acts from the ground and which passes through the center of the wheel. If bearing C acts as a simple support and the effect of transverse shear due to P is negligible, determine the maximum force P (in kN) that can be applied to the wheel. Consider a factor of safety n = 2.5. Use the maximum energy of distortion failure criterion and do the analysis on bar AB (torsion bar) in the section where the bearing is.
A steel rod is subjected to a gradually applied load (F) which gave a rise to a maximum stress of 200 MPa. The rod is 250 mm long and one part of its length is square and the remainder is cireular with a diameter of 25 mm. If the total strain energy in the rod and modulus elasticity of the material is 1.3 J and 200 GPa, detemine the following: 4.3 The length of the square portion of the bar The suddenly applied load that will induce the same amount of energy 4.4 4.5 The load that falls from a height of 8 mm induces 1,3 J in the bar.
2. A composite rod of overall length of 200 mm comprised of a steel rod and brass rod attached rigidly to the end. The diameter and length of the steel rod are given as 10 mm and 120 mm, respectively, the diameter and the length of the brass rod as 20 mm and 80 mm respectively. The rod is used as a tie in a link mechanism and the strain in the brass rod is limited to 0,53x 10-3. Given that the total extension of the composite rod must not exceed 0,162 4 mm and E for steel is 200 GPa, respectively. Calculate: d. Modulus of elasticity for the brass.
2. A composite rod of overall length of 200 mm comprised of a steel rod and brass rod attached rigidly to the end. The diameter and length of the steel rod are given as 10 mm and 120 mm, respectively, the diameter and the length of the brass rod as 20 mm and 80 mm respectively. The rod is used as a tie in a link mechanism and the strain in the brass rod is limited to 0,53x 10-3. Given that the total extension of the composite rod must not exceed 0,162 4 mm and E for steel is 200 GPa, respectively. Calculate: a. Strain in the steel rod
2. A composite rod of overall length of 200 mm comprised of a steel rod and brass rod attached rigidly to the end. The diameter and length of the steel rod are given as 10 mm and 120 mm, respectively, the diameter and the length of the brass rod as 20 mm and 80 mm respectively. The rod is used as a tie in a link mechanism and the strain in the brass rod is limited to 0,53x 10-3. Given that the total extension of the composite rod must not exceed 0,162 4 mm and E for steel is 200 GPa, respectively. Calculate: b. Load carried by the steel and brass rods
2. A composite rod of overall length of 200 mm comprised of a steel rod and brass rod attached rigidly to the end. The diameter and length of the steel rod are given as 10 mm and 120 mm, respectively, the diameter and the length of the brass rod as 20 mm and 80 mm respectively. The rod is used as a tie in a link mechanism and the strain in the brass rod is limited to 0,53x 10-3. Given that the total extension of the composite rod must not exceed 0,162 4 mm and E for steel is 200 GPa, respectively. Calculate: a. Strain in the steel rod b. Load carried by the steel and brass rods d. Modulus of elasticity for the brass.
4. An alloy circular bar rigidly fixed at its both ends uniformly tapers from 90 mm to 60 mm from one end to another. What will be the maximum stress developed in the bar, when its temperature is raised through 20 K? Take E and a for the bar material as 150 GPa and 12 x 10 /K. Also find the maximum stress when the bar is lowered by the same temperature. [Ans. 54 MPa (Compn.): 54 MPa (Tension)]
1 (c) Determine the maximum shear stress for the member shown in figure below. The lengths and diameters of the member are: I = 500 mm; The member supports a load of 2000 N vertically downwards. Neglect transverse shear. 2 = 150 mm; d = d2 50 mm ....-. 2 1 F=2000
A rectangular steel block is 3 inches long in the x direction, 2 inches long in the y direction, and 4 inches long in the z direction. The block is subjected to a triaxial loading of three uniformly distributed forces as floows; 48 kips tension in the x directio, 60 kips compression in the y direction, and 54 kips tension in the z direction. If v = 0.30 and E = 29 x 106 psi, determine the single uniformly distributed load in the x direction that would produce the same deformation in the y direction as the original loading.