Note: J3 = J2 46 mm G3 = G2 4.93×10 mm (1) 16 kN-m 50 GPa (2) 34 mm %3D (3) 2.10x106 mm 900 mm 35 GPa %3D 900 mm A composite torsion member consists of a tubular shell (1) bonded to length AB of a continuous solid T1 kN-m shaft that extends from A to C, which is labeled T2 kN-m (2) and (3). A concentrated torque T is applied to MPa free end C of the shaft in the direction shown. MPa Determine the internal torques and shear stresses PC rad in shell (1) and core (2) (i.e., between A and B). 1st 2nd 3rd Enter Also, determine the rotation angle at end C. attemnt Shaft properties

Note: J3 = J2 46 mm G3 = G2 4.93×10 mm (1) 16 kN-m 50 GPa (2) 34 mm %3D (3) 2.10x106 mm 900 mm 35 GPa %3D 900 mm A composite torsion member consists of a tubular shell (1) bonded to length AB of a continuous solid T1 kN-m shaft that extends from A to C, which is labeled T2 kN-m (2) and (3). A concentrated torque T is applied to MPa free end C of the shaft in the direction shown. MPa Determine the internal torques and shear stresses PC rad in shell (1) and core (2) (i.e., between A and B). 1st 2nd 3rd Enter Also, determine the rotation angle at end C. attemnt Shaft properties

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter5: Stresses In Beams (basic Topics)

Section: Chapter Questions

Problem 5.9.5P: A sign for an automobile service station is supported by two aluminum poles of hollow circular cross...

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A sign for an automobile service station is supported by two aluminum poles of hollow circular cross section, as shown in the figure. The poles are being designed to resist a wind pressure of 75 lb/ft" against the full area of the sign. The dimensions of the poles and sign are hx= 20 ft, /r =5 ft, and h = 10 ft. To prevent buckling of the walls of the poles, the thickness e is specified as one-tenth the outside diameter d. (a) Determine the minimum required diameter of the poles based upon an allowable bending stress of 7500 psi in the aluminum. (b) Determine the minimum required diameter based upon an allowable shear stress of 300 psi.
Repeat Problem 11.2-14 using L = 12 ft, ß = 0.25 kips/in., ßRl= 1.5ßL2, and ßR2= 2 ßR1.
Solve the preceding problem for an aluminum column with b = 6,0 in., t = 0.5 in., P = 10 kips, and E = 10.6 × 106 ksi. The defied ion at the top is limited to 2.0 in.
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 vertical pole of aluminum is fixed at the base and pulled at the top by a cable having a tensile force T(see figure). The cable is attached at the outer edge of a stiffened cover plate on top of the pole and makes an angle a = 20° at the point of attachment. The pole has length a = 2.5 m and a hollow circular cross section with an outer diameter d2= 280 mm and inner diameter d1= 220 mm. The circular cover plate has diameter 1.5d2 Determine the allowable tensile force Tallow in the cable if the allowable compressive stress in the aluminum pole is 90 MPa.
Repeat Problem 11.2-3 assuming that R= 10 kN · m/rad and L = 2 m.
Rigid bar ACB is supported by an elastic circular strut DC having an outer diameter of 15 in. and inner diameter of 14.4 in. The strut is made of steel with a modulus elasticity of E = 29,000 ksi. Point load P = 5 kips is applied at B. Calculate the change in length of the circular strut DC. What is the vertical displacement of the rigid bar at point B?
A steel column ( E = 30 X 103 ksi) that is fixed at the base and free at the top is constructed of a W8 x 35 wide-flange member (sec figure). The column is 9.0 ft long. The force P acting at the top of the column has an eccentricity e = 1.25 in. If P = 40 kips, what is the maximum compressive stress in the column? If the yield stress is 36 ksi and the required factor of safety with respect to yielding is 2.1, what is the allowable load Pallow?
AW310 × 74 wide-flange steel column with length L = 3.8 m is fixed at the base and free at the top (see figure). The load P acting on the column is intended to be centrally applied, but because of unavoidable discrepancies in construction, an eccentricity ratio of 0.25 is specified. Also, the following data are supplied: E = 200 GPa, y = 290 MPa, and P = 310 kN. What is the maximum compressive stress max in the column? What is the factor of safety n with respect to yielding of the steel?
Compare the angle of twist 1 for a thin-walled circular tube (see figure) calculated from the approximate theory for thin-walled bars with the angle of twist 2 calculated from the exact theory of torsion for circular bars, Express the ratio 12terms of the non-dimensional ratio ß = r/t. Calculate the ratio of angles of twist for ß = 5, 10, and 20. What conclusion about the accuracy of the approximate theory do you draw from these results?
A pinned-end strut of aluminum (E = 10,400 ksi) with a length L = 6 ft is constructed of circular tubing with an outside diameter d = 1 in. (sec figure). The strut must resist an axial load F = 4 kips with a factor of safety n = 2.0 with respect to the critical load. Determine the required thickness t of the tube.
A pinned-end column with a length L = 18 ft is constructed from a W12 x 87 wide-flange shape (sec figure). The column is subjected to a centrally applied load P1=180 kips and an eccentrically applied load P2=15 kips. The load P2acts at a distance s = 5.0 in. from the centroid of the cross section. The properties of the steel arc E = 29,000 ksi and y = 36 ksi. Calculate the maximum compressive stress in the column. Determine the factor of safety with respect to yielding.