A thin-walledbeam of hollow circular cross-section shown below is subject to both torsional and transverse loads. The outside diameter do= 100mm and wall thickness t= 5mm. At a specific cross-section,the bending moments are My= 600 N.,m, Mz= 950 N.mand torsional moment is Mx=T=500 N.m. Calculate the principal stresses and the maximum shear stress at point A. Assume angle θ is 59 (degrees). Ignore transverse shear stress at point A. Use the closed thin-walled theory to solve for torsional shear stress.

A thin-walledbeam of hollow circular cross-section shown below is subject to both torsional and transverse loads. The outside diameter do= 100mm and wall thickness t= 5mm. At a specific cross-section,the bending moments are My= 600 N.,m, Mz= 950 N.mand torsional moment is Mx=T=500 N.m. Calculate the principal stresses and the maximum shear stress at point A. Assume angle θ is 59 (degrees). Ignore transverse shear stress at point A. Use the closed thin-walled theory to solve for torsional shear stress.

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 3.11.4P: A thin-walled steel tube of rectangular cross section (see figure) has centerline dimensions b = 150...

See similar textbooks

Similar questions

A cantilever beam(Z, = 6 ft) with a rectangular cross section (/> = 3.5 in., h = 12 in.) supports an upward load P = 35 kips at its free end. (a) Find the state of stress ((7T, o^., and r in ksi) on a plane-stress element at L/2 that is i/ = 8 in. up from the bottom of the beam. Find the principal normal stresses and maximum shear stress. Show these stresses on sketches of properly oriented elements. (b) Repeat part (a) if an axial compressive centroidal load N = 40 kips is added at B
. A segment of a generator shaft with a hollow circular cross section is subjected to a torque T = 240 kip-in, (see figure). The outer and inner diameters of the shaft arc 8.0 in, and 6.25 in., respectively. What is the maximum permissible compressive load /'that can be applied to the shaft if the allowable in-plane shear stress is rAi(m= 6250 psi
A solid circular bar is fixed at point A. The bar is subjected to transverse load V = 70 lb and torque T = 300 lb-in. at point B. The bar has a length L = 60 in. and diameter d = 3 in. Calculate the principal normal stresses and the maximum shear stress at clement 1 located on the bottom surface of the bar at fixed end A (see figure), Assume that element 1 is a sufficient distance from support A so that stress concentration effects are negligible
A stepped shaft (see figure) has diameter D2= 1.5 in, and a full quarter-circular fillet. The allowable shear stress is 15,000 psi and the load T = 4800 1b-in. What is the smallest permissible diameter D1?
A solid circular bar of steel (G = 1L4 × 106 psi) with length L = 30 in, and diameter d = 1.75 in, is subjected to pure torsion by torques T acting at the ends (see figure). Calculate the amount of strain energy V stored in the bar when the maximum shear stress is 4500 psi. From the strain energy, calculate the angle of twist 0 (in degrees).
A thin-walled steel tube of rectangular cross section (see figure) has centerline dimensions b = 150 mm and h = 100 mm. The wall thickness t is constant and equal to 6.0 mm. Determine the shear stress in the tube due to a torque T = 1650 N · m. Determine the angle of twist (in degrees) if the length L of the tube is 1.2 m and the shear modulus G is 75 GPa.
A thin-walled steel tube having an elliptical cross section with constant thickness t (see figure) is subjected to a torque T = 18 kip-in. Determine the shear stress and the rate of twist in degrees per inch) if G = 12 × 106 psi, t = 0.2 in., a = 3 in., and b = 2 in. Note: See Appendix E, Case 16, for the properties of an ellipse.
A beam with a width h = 6 in. and depth h = 8 in. is simply supported at A and B. The beam has a length L = 10 ft and is subjected to a linearly varying distributed load with peak intensity q0= 1500 lb/ft. Calculate the state of plane stress at point C located 3 in. below the top of the beam and 0.1 ft to the left of point B. Also find the principal stresses on element C. Neglect the weight of the beam.
A wood pole with a solid circular cross section (d = diameter) is subjected to a triangular distributed horizontal force of peak intensity q0= 20 lb/in. (see figure). The length of the pole is L = 6 ft, and the allowable stresses in the wood arc 1900 psi in bending and 120 psi in shear. Determine the minimum required diameter of the pole based upon (a) the allowable bending stress, and (b) the allowable shear stress.
A hollow steel shaft used in a construction auger has an outer diameter d2= 6.0 in. and inner diameter d1= 4.5 in. (see figure). The steel has a shear modulus of elasticity G = 11.0 × 106 psi. For an applied torque of 150 kip-in., determine the following quantities: shear stress at the outer surface of the shaft, shear stress at the inner surface, and rate of twist (degrees per unit of length). Also, draw a diagram showing how the shear stresses vary in magnitude along a radial line in the cross section.
-11 A solid steel bar (G = 11.8 X 106 psi ) of diameter d = 2,0 in. is subjected to torques T = 8.0 kip-in. acting in the directions shown in the figure. Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.
A long, thin-walled tapered tube AB with a circular cross section (see figure) is subjected to a torque T. The tube has length L and constant wall thickness t. The diameter to the median lines of the cross sections at the ends A and B are dAand dB, respectively. Derive the following formula for the angle of twist of the tube: Hint: If the angle of taper is small, you may obtain approximate results by applying the formulas for a thin-walled prismatic tube to a differential element of the tapered tube and then integrating along the axis of the tube.