A bicycle chain consists of a series of small links, where each is 12 mm long between the centres of the pins (see figure). You might have to observe a bicycle chain and observe its construction. The pedal crank arm has a length L = 162 mm centre to centre as shown and the sprocket (toothed gearwheel) radius R = 90 mm. 1.1 Calculate the tensile force T in the chain due to a force F = 800 N applied to one of the pedals. /4/ 1.2 Calculate the average shear stress τ in the pins.

A bicycle chain consists of a series of small links, where each is 12 mm long between the centres of the pins (see figure). You might have to observe a bicycle chain and observe its construction. The pedal crank arm has a length L = 162 mm centre to centre as shown and the sprocket (toothed gearwheel) radius R = 90 mm. 1.1 Calculate the tensile force T in the chain due to a force F = 800 N applied to one of the pedals. /4/ 1.2 Calculate the average shear stress τ in the pins.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter3: Torsion

Section: Chapter Questions

Problem 3.8.13P: A solid steel bar of diameter d1= 1.50 in. is enclosed by a steel tube of outer diameter d3= 2.25...

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A circular tube of inner radius r1and outer radius r2is subjected to a torque produced by forces P = 900 lb (see figure part a). The forces have their lines of action at a distance b = 5.5 in. from the outside of the tube. (a) If the allowable shear stress in the tube is 6300 psi and the inner radius r1= 1.2 in., what is the minimum permissible outer radius r2? (b) If a torsional spring of stiffness = 450 kip-in./rad is added at the end of the tube (see figure part b), what is the maximum value of forces P lithe allowable shear stress is not to be exceeded? Assume that the tube has a length of L 18 in., outer radius of r2= 1.45 in. and shear modulus G = 10.800 ksi. Hint: Consider the tube and torsional spring as “springs in parallel.”
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 vertical pole of solid, circular cross section is twisted by horizontal forces P = 5kN acting at the ends of a rigid horizontal arm AB (see figure part a). The distance from the outside of the pole to the line of action of each force is c = 125 mm (sec figure part b) and the pole height L = 350 mm. (a) If the allowable shear stress in the pole is 30 MPa, what is the minimum required diameter dminof the pole? (b) What is the torsional stiffness of the pole (kN · m/rad)? Assume that G = 28 GPa. (c) If two translation al springs, each with stiffness k =2550 kN/m, are added at 2c/5 from A and B (see figure part c), repeat part (a) to find dmin. Hint: Consider the pole and pair of springs as "springs in parallel."
A uniform bar AB of weight W = 25 N is supported by two springs, as shown in the figure. The spring on the left has a stiffness k[= 300 N/m and natural length Lt=250 mm. The corresponding quantities for the spring on the right are k2= 400 N/m and L^ = 200 mm. The distance between the springs is L = 350 mm, and the spring on the right is suspended from a support that is a distance it = SO mm below the point of support for the spring on the left. Neglect the weight of the springs. (a) At what distance x from the left-hand spring (figure part a) should a load P = 18 N be placed in order to bring the bar to a horizontal position? (b) If P is now removed, what new value of k{is required so that the bar (figure part a) will hang in a horizontal position underweight If? (c) If P is removed and kt= 300 N/m. what distance b should spring ktbe moved to the right so that the bar (figure part a) will hang in a horizontal position under weight II"? (d) If the spring on the left is now replaced by two springs in series (kt= 300 N/m, kt) with overall natural length Lt= 250 mm (see figure part b). what value of k; is required so that the bar will hang in a horizontal position under weight IF?
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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?
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