Chapter 5.10, Problem 144P

The copper pipe has an outer diameter of 40 mm and an inner diameter of 37 mm. If it is tightly secured to the wall at A and 3 torques are applied to it as shown, determine the absolute maximum shear stress developed in the pipe. Given the shear modulus G = 37 GPa for copper and the segmental lengths of the pipe, calculate the angle of twist of point D with respect to point A| B Length: AB = 0.6 m ´ 30 N-m 20 N-m BC = 0.6 m CD = 1.2 m 80 N-m

The rod has a circular cross-section with a polar moment of inertia J and moment of inertia I. If a vertical force P is applied at A, determine the vertical displacement at this point. Consider the strain energy due to bending andtorsion. The material constants are E and G.

The copper pipe has an outer diameter of 3 in. and an inner diameter of 2.50 in. If it is tightly secured to the wall at C and it is subjected to the uniformly distributed torque along its entire length, determine the absolute maximum shear stress in the pipe. Discuss the validity of this result.

The shaft consists of three concentric tubes, each made from the same material and having the inner and outer radii as shown. If the torque of T=800 N•m is applied to the rigid disk fixed to its end, determine the maximum shear stress in the shaft. S •5-9. The shaft consists of three concentric tubes, each made from the same material and having the inner and outer radii shown. If a torque of T the rigid disk fixed to its end, determine the maximum shear stress in the shaft. = 800 N• m is applied to T= 800 N.m r = 20 mm ro = 25 mm 2 m r; = 26 mm ro = 30 mm %3D r; = 32 mm 38 mm Prob. 5-9

If the solid shaft AB to which the valve handle is attached is made of C83400 red brass and has a diameter of 10 mm, determine the maximum couple forces F that can be applied to the handle just before the material starts to fail. Take 7allow = 40 MPa. What is the angle of twist of the handle? The shaft is fixed at A. 150 mm 150 mm 150 mm

The friction pad A is used to support the member,which is subjected to an axial force of P = 2 kN. Thepad is made from a material having a modulus ofelasticity of E = 4 MPa and Poisson’s ratio n = 0.4.If slipping does not occur, determine the normaland shear strains in the pad. The width is 50 mm.Assume that the material is linearly elastic. Also,neglect the effect of the moment acting on the pad.

The copper pipe has an outer diameter of 3 in. and an inner diameter of 2.5 in. If it is tightly secured to the wall at C and a uniformly distributed torque is applied to it as shown, determine the shear stress at points A and B. These points lie on the pipe’s outer surface. Sketch the shear stress on volumeelements located at A and B.

The shaft has a radius c and is subjected to a torque per unit length of t0, which is distributed uniformly over the shaft’s entire length L. If it is fixed at its far end A, determine the angle of twist f of end B. The shear modulus is G.

The steel shaft has a radius of r=50 mm. Determine the torque (T) applied to the shaft if the two strain gages attached to the shaft surface record the deformations ?? ′ = −80 (10-6) and ?? ′ = 80 (10-6) Take E = 200 GPa, ν = 0.3. (Hint: you can assume that under torsional moment there is no deformation in x and y direction)