A solid bar having a diameter 150 mm is to be replaced by a square tube having a cross-sectional dimension shown in the figure. A. Determine the required dimension "a" if the thickness is 10mm so that the maximum shear stress in the tube will not exceed the maximum shear stress in the solid bar. B. Determine the shear stress in the tube if it is subjected to a torque T = 12 kN.m. C. Determine the angle of twist in degrees of the tube if the length of the tube is 800mm and the shear modulus is 75GPa, T = 12 kN.m. 1. A solid bar having a diameter 150 mm is to be replaced by a square tubehaving a cross-sectional dimension shown in the figure.A. Determine the required dimension "a" if thethickness is 10mm so that the maximum shearstress in the tube will not exceed the maximumshear stress in the solid bar.B. Determine the shear stress in the tube if itis subjected to a torque T = 12 kN m.C. Determine the angle of twist in degrees of thetube if the length of the tube is 800mm andthe shear modulus is 75GP%, T = 12 kN m.

Answered: Image /qna-images/answer/6f95ccb2-6fc0-423c-bc25-ba28259121d9.jpg

A solid bar having a diameter 150 mm is to be replaced by a square tube having a cross-sectional dimension shown in the figure. A. Determine the required dimension "a" if the thickness is 10mm so that the maximum shear stress in the tube will not exceed the maximum shear stress in the solid bar. B. Determine the shear stress in the tube if it is subjected to a torque T = 12 kN.m. C. Determine the angle of twist in degrees of the tube if the length of the tube is 800mm and the shear modulus is 75GPa, T = 12 kN.m.

A solid bar having a diameter 150 mm is to be replaced by a square tube having a cross-sectional dimension shown in the figure. A. Determine the required dimension "a" if the thickness is 10mm so that the maximum shear stress in the tube will not exceed the maximum shear stress in the solid bar. B. Determine the shear stress in the tube if it is subjected to a torque T = 12 kN.m. C. Determine the angle of twist in degrees of the tube if the length of the tube is 800mm and the shear modulus is 75GPa, T = 12 kN.m.

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 3.11.2P: A solid circular bar having diameter d is to be replaced by a rectangular tube having...

See similar textbooks

Similar questions

The hollow drill pipe for an oil well (sec figure) is 6,2 in. in outer diameter and 0.75 in. in thickness. Just above the bit, the compressive force in the pipe (due to the weight of the pipe) is 62 kips and the torque (due to drilling) is 185 kip-in. Determine the maximum tensile, compressive, and shear stresses in the drill pipe.
Solve the preceding problem if the norm al and shear stresses acting on the element are sx = 2100 kPa, sy= 300 kPa, and txy= -560 kPa, and the seam is oriented at an angle of 22.5° to the clement.
A punch for making a slotted hole in ID cards is shown in the figure part a. Assume that the hole produced by the punch can be described as a rectangle (12 mm X 3 mm) with two half circles (r = 1.5 mm) on the left and the right sides. If P = 10 N and the thickness of the ID card is 1 mm, what is the average shear stress in the card?
A steel punch consists of two shafts: upper shaft and lower shaft. Assume that the upper shaft has a diameter d1= 24 mm and the bottom shaft has a diameter d2= 16 mm. The punch is used to insert a hole in a 4 mm plate, as shown in the figure. If a force P - 70 kN is required to create the hole, what is the average shear stress in the plate and the average compressive stress in the upper and lower shaft of the punch?
‘7.3-11 The stresses on an element are sx= -300 psi and sy= 600 psi. Find the maximum shear stresses on the element and show them on a sketch of a properly oriented clement.
A capped cast-iron pipe is compressed by a brass rod, as shown. The mil is turned until it is just snug, then add an additional quarter turn to pre-compress the cast-iron pipe. The pitch of the threads of the bolt ap = 52 mils (a mil is one-thousandth of an inch). Use the numerical properties provided. (a) What stresses a and arwill be produced in the cast-iron pipe and brass rod. respectively, by the additional quarter turn of the nut? (b) Find the bearing stress ahbeneath the washer and the shear stress t(in the steel cap.
The stresses acting on an element are x= 750 psi, y= 600 psi, and xy = 400 psi. Determine the principal stresses and show them on a sketch of a properly oriented element.
A sign is supported by a pipe (see figure) having an outer diameter 110 mm and inner diameter 90 mm. The dimensions of the sign are 2.0 m X 1.0 m, and its lower edge is 3.0 m above the base. Note that the center of gravity of the sign is 1.05 m from the axis of the pipe. The wind pressure against the sign is 1.5 kPa. Determine the maximum in-plane shear stresses due to the wind pressure on the sign at points /I, B, and C, located on the outer surface at the base of the pipe.
A tie-down on the deck of a sailboat consists of a bent bar boiled at both ends, as shown in the figure. The diameter dBof the bar is 1/4 in., the diameter D Wof the washers is 7/8 in., and the thickness is of the fiberglass deck is 3/8 in. If the allowable shear stress in the fiberglass is 300 psi, and the allowable bearing pressure between the washer and the fiberglass is 550 psi, what is the allowable load P allowon the tie-down?
A thin-walled rectangular tube has uniform thickness t and dimensions a x b to the median line of the cross section (see figure). How does the shear stress in the tube vary with the ratio = a/b if the total length Lmof the median line of the cross section and the torque T remain constant? From your results, show that the shear stress is smallest when the tube is square (ß = 1).
When drilling a hole in a table leg, a furniture maker uses a hand-operated drill (see figure) with a bit of diameter d = 4.0 mm. If the resisting torque supplied by the table leg is equal to 0.3 N · m, what is the maximum shear stress in the drill bit? If the allowable shear stress in the drill bit is 32 MPa, what is the maximum resisting torque before the drill binds up? If the shear modulus of elasticity of the steel is G = 75 GPa, what is the rate of twist of the drill bit (degrees per meter)?
An aluminum tube has inside diameter dx= 50 mm, shear modulus of elasticity G = 27 GPa, v = 0.33, and torque T = 4.0 kN · m. The allowable shear stress in the aluminum is 50 MPa, and the allowable normal strain is 900 X 10-6. Determine the required outside diameter d2 Re-compute the required outside diameter d2, if allowable normal stress is 62 MPa and allowable shear strain is 1.7 X 10-3.