A bar in the shape of a solid truncated cone of circular cross-section is situated between two rigid supports which constrain the bar from any change of axial length. The temperature of the entire bar is then raised by AT. Assume that the cross-sections perpendicular to the longitudinal axis of symmetry remain plane and neglect localized end effects due to the end supports. Determine the normal stresses at any point in the bar.

A bar in the shape of a solid truncated cone of circular cross-section is situated between two rigid supports which constrain the bar from any change of axial length. The temperature of the entire bar is then raised by AT. Assume that the cross-sections perpendicular to the longitudinal axis of symmetry remain plane and neglect localized end effects due to the end supports. Determine the normal stresses at any point in the bar.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

The triangular solid plate ABC is restrained by rod (1) at A and pin support at B. After applying the force P, the solid plate tilts around pin B and after closing the gap = 1.9 mm, pushes element (2). What is the strain in rod (1) if the internal strain in element (2) is E2 = -1020 pe? [L₁=620 mm, L₂= 680 mm, a = 300 mm, b = 320 mm, gap= 1.9 mm] L AD (2
b) A cylindrical rod AB is made of aluminum is connected at B to a brass qylindrical rod BCD as shown in Figure 8. The shear modulus, G of aluminum rod AB is given by 27 GPa and the brass rod BCD of 39 GPa. The torsional reactions, TA and Ts are located at the ends of A and B, respectively. Given the portion CD of the brass rod is hollow and has an inner diameter of 40 mm, examine the angle of twist at A. 60 mm Tg = 1600 N - m 36 mm TA = 800 N m 250 mm 375 mm A 400 mm Figure 8
Q1. 1.) Determine the state of stresses at an orientation of 20 degree clockwise from the element x-axis shown. у-аxis 2 MPa 3 MPa х-ахis 4 MPa
7. The rigid bar ABCD of negligible weight is initially horizontal, and the steel rods attached at A and C are stress-free. The load P is then applied and there is a temperature change in the steel rods. P = 35 kips with the stresses in the two steel rods equal. Assume that there is no buckling in the rods. The coefficient of linear expansion is 6.5 x 10^-6 per degree F and E = 29 x 10^6 psi for steel. A = 0.5 in.² 3 ft | A D 4 ft 4 ft- * 2 ft →+ 2 ft → A = 0.75 in.² Determine the change in temperature. Indicate increase or decrease in temperature. Your answer
2.43 Show that if the rubber sleeve in Prob. 2.42 is thick, the displacement of the shaft is D+ 2t In 2πGL P D
2.24 The biaxial loading is subjected to the polyethylene sheet as shown. Calculate the sides of AB and AC as a result of the elongations. E = 300 ksi and v = 0.4 are the properties of polyethylene. %3D 1.4ksi D. Y 2ft 3ft A 1.4ksi 2.5ksi B 2.5ksi
At a temperature of 34°F, a 0.06 in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [a = 12.5 x 10-6/°F] and bar (2) is stainless steel [a = 7.3 x 10-6/°F]. The supports at A and C are rigid. Determine the lowest temperature at which the two bars contact each other. (1) 33m B (2) Answer: Final temperature = 55 in. -0.06. gap °F.
A two member truss ABC is shown in the figure. The force (in kN) transmitted in member AB is
The state of strain at the point on the member has components of Px = 180(10-6), P y = -120(10-6), and gxy = -100(10-6). Use the strain transformation equations to determine (a) the in-plane principal strains and (b) the maximum in-plane shear strain and average normal strain. Ineach case specify the orientation of the element and show how the strains deform the element within the x–y plane.
The rigid bar AB of negligible weight is supported by a pin at O. When the two steel rods are attached to the ends of the bar, there is a gap A = 4 mm between the lower end of the left rod and its pin support at C. %3D Compute the stress in the left rod after its lower end is attached to the support. The cross-sectional areas are 300 mm2 for rod AC and 250 mm? for rod BD. Use E = 200 GPa for steel. A В 0.75 m 1.5 m > 2 m D
From the given figure Solve the following: Let P = 30 Find: Vertical reaction at CHorizontal reaction at CAxial force at member AB
P= 30, Determine the interactions at the following beam supports