3. A spring wire with diameter of 6 mm in a circular arc shape was initially set on the horizontal plane. One end is fixed at point B and the other end A is free. The radius of the arc R-80 mm and the center angle of the arc 0-60°. The wire is made of a steel with modulus of elasticity: 200 GPa and Poisson's ratio: 0.29. Considering that F=25 N which is applied vertically downward at A, find the total deflection at A. Hint: I = π (64)/64 = 63.62 mm¹. Vo R BX F

3. A spring wire with diameter of 6 mm in a circular arc shape was initially set on the horizontal plane. One end is fixed at point B and the other end A is free. The radius of the arc R-80 mm and the center angle of the arc 0-60°. The wire is made of a steel with modulus of elasticity: 200 GPa and Poisson's ratio: 0.29. Considering that F=25 N which is applied vertically downward at A, find the total deflection at A. Hint: I = π (64)/64 = 63.62 mm¹. Vo R BX F

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 2.8.14P: A rigid bar AB having a mass M = 1.0 kg and length L = 0.5 m is hinged at end A and supported at end...

See similar textbooks

Similar questions

The L-shaped arm ABCD shown in the figure lies in a vertical plane and pivots about a horizontal pin at A. The arm has a constant cross-sectional area and total weight W. A vertical spring of stiffness k supports the arm at point B. (a) Obtain a formula for the elongation of the spring due to the weight of the arm. (b) Repeat part (a) if the pin support at A is moved to D.
A long, slender bar in the shape of a right circular cone with length L and base diameter d hangs vertically under the action of its own weight (see figure). The weight of the cone is W and the modulus of elasticity of the material is E. Derive a formula for the increase S in the length of the bar due to its own weight. (Assume that the angle of taper of the cone is small.)
A polyethylene tube (length L) has a cap that when installed compresses a spring (with under-formed length L1) by an amount ?? = (L1 = L). Ignore deformations of the cap and base. Use the force at the base of the spring as the redundant. Use numerical properties given in the boxes. (a) What is the resulting Force-in the spring, Fk? (b) What is the resulting Force in the tube, Ftl (c) What is the filial length of the tube, Lf? (d) What temperature change ?T inside the tube will result in zero force in the spring
Wires B and C are attached to a support at the left-hand end and to a pin-supported rigid bar at the right-hand end (see figure). Each wire has cross-sectional area A =0.03 in2 and modulus of elasticity E = 30 X 106 psi. When the bar is in a vertical position, the length of each wire is L = 80 in. However, before being attached to the bar, the length of wire B was 79.98 in. and wire C was 79.95 in. Find the tensile forces TBand Tc in the wires under the action of a force P = 700 lb acting at the upper end of the bar.
Solve the preceding problem if the collar has mass M = 80 kg, the height h = 0.5 m, the length L = 3.0 m, the cross-sectional area A = 350mm2. and the modulus of elasticity E = 170 GPa.
A bimetallic bar (or composite bar) of square cross sec lion with dimensions 2b X lb is construe ted of two different metals having module of elasticity E2and E2(see figure). The two parts of the bar have the same cross-sectional dimensions. The bar is compressed by forces P acting through rigid end plates. T h e line of action of t he loads has an eccentricity e of such magnitude that each part of the bar is stressed uniformly in compression. (a) Determine the axial forces Ptand P2in the two parts of the bar. (b} Determine the eccentricity e of the loads. (c) Determine the ratio C|/tr2 of the stresses in the two parts of the bar.
Solve the preceding problem for a steel pipe column (E = 210 GPa) with length L = 1.2 m, inner diameter d2= 36 mm, and outer diameter d2=40 mm.
A slightly tapered bar AB of solid circular crass section and length L is supported at end B and subjected to a tensile load P at the free end A. The diameters of the bar at ends A and B are dAand dB. respectively. Determine the length of the bar if the elongation of the bar due to the load P = 45 kips is 0.02 in. Assume that E = 10,400 ksi.
.17 A mountain-bike rider going uphill applies torque T = Fd(F = l5lb, d = 4 in.) to the end of the handlebars ABCD by pulling on the handlebar extenders DE. Consider the right half of the handlebar assembly only (assume the bars are fixed at the fork at A). Segments AB and CD are prismatic with lengths L, = 2 in.andL3 = 8.5 in, and with outer diameters and thicknesses d01 = 1.25 in. 101 = 0.125 in. and d03 = O.87in.,i03 = 0.ll5in, respectively as shown. Segment BC’ of length L, = 1.2 in. however. is tapered, and outer diameter and thickness vary linearly between dimensions at B and C. Consider torsion effects only. Assume G = 4000 ksi is constant. Derive an integral expression for the angle of twist of half of the handlebar tube when it is subjected to torque T = Fd acting at the end. Evaluate ‘b1-, for the given numerical1ues.
A rigid bar AB having a mass M = 1.0 kg and length L = 0.5 m is hinged at end A and supported at end B by a nylon cord BC (see figure). The record has cross-sectional area A = 30 mm2. length b = 0.25 m. and modulus of elasticity E = 2.1 GPa. If the bar is raised to its maximum height and then released, what is the maximum stress in the cord?
The fixed-end bar ABCD consists of three prismatic segments, as shown in the figure. The end segments have a cross-sectional area A1= 840 mm2and length Lt= 200 mm. The middle segment has a cross-sectional area A2= 1260 mm2 and length L2= 250 mm. Loads PBand Pcare equal to 25.5 kN and 17.0 kN, respectively. (a) Determine the reactions RAand RDat the fixed supports. (b) Determine the compressive axial force FBCin the middle segment of the bar.
The device shown in the figure consists of a prismatic rigid pointer ABC supported by a uniform translational spring of stiffness k = 950 N/m. The spring is positioned a distance P = 165 nun from the pinned end A of the pointer. The device is adjusted so that, when there is no load P, the pointer reads zero on the angular scale. (a) If the load P = 11 N, al what distance .v should the load be placed so that the pointer will read ?? = 2.5° on the scale (see figure part a)? (b) Repeal part (a) if a rotational spring E1= kb-6 is added al A (see figure part b). (c) Lel.x = 7b/8.What is P maxif 0 cannot exceed 2"? Include spring krin your analysis. (d) Now, if the weight of the pointer ABC is known to be W =3N and the weight or the spring is Ws= 2.75 N, what initial angular position (Left in degrees) of the pointer will result in a zero reading on the angular scale once the pointer is released from rest? Assume P = kr=0. (e) If the pointer is rotated lo a vertical position (see figure part c), find the required load P applied at mid-height of the pointer that will result in a pointer reading of 0 = 2.5" on the scale. Consider the weight of the pointer W. in your analysis.