ADU. ENG. FAC. CIVIL ENG. DEPT. STRENGTH OF MATERIALS HW.#3 Due:20.11.2014 NAME SURNAME 1 2 ID No TOTAL Q 1. 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 three torques are applied to it as shown, determine the absolute maximum shear stress developed in the pipe. (50 p) B C D Internal torques: TCD=80 N.m; TBC=60 N.m; TAB=90 N.m Absolute maximum shear stress is observed at the outer radius (co=20 mm) of the part where internal torque is highest (part AB) Absolute max. torsional shear stress: 1 Asst.Prof.Dr. Emre AKIN ADU. ENG. FAC. CIVIL ENG. DEPT. STRENGTH OF MATERIALS HW.#3 Due:20.11.2014 Q 2. The assembly shown is composed of a steel cylinder rod (AB) with a diameter of 25 mm and aluminum rod (BC) with a diameter of 50 mm. The lengths of members AB and BC are 1000 and 500 mm, respectively. Also, member ADE is rigidly connected to this assembly at A. There is a distributed loading between D and E with a value of 1 kN/m. a. Determine the absolute maximum torsional shear stresses on steel member AB and aluminum (25 p) member BC. Also find the total angle of twist of the assembly. (G =76 GPa, G =25 GPa) st al b. The ultimate tensile strength (failure stress in tension) of steel and aluminum are given as 400 (25 p) and 300 MPa, respectively. It is also known that the ultimate shear strength (failure stresss in shear) of both steel and aluminum may be assumed as 60% of the ultimate tensile strength of both metals. If the factor of safety (F.S.) for both materials is given as 1.5, check the safety of these steel and aluminum members considering only torsion. Note: There is a rigid connection between all members and at support C. C B 1 kN/m A D E a. The torque applied on the assembly: T=(1 kN/m) x (0.3 m)x [(0.2+0.3/2) m]=0.105 kN.m=105000 N.mm The polar moment of inertia of the members: The maximum torsional shear stress occurs at the outer radius of each member: 2 Asst.Prof.Dr. Emre AKIN ADU. ENG. FAC. CIVIL ENG. DEPT. STRENGTH OF MATERIALS HW.#3 Due:20.11.2014 The total angle of twist due to torsion: ∑ Minus sign indicates the twist is in the direction such that the right hand thumb directs inward to the members. b. The ultimate shear strength of steel and aluminum: The allowable shear strength of steel and aluminum: Safety check for both members: ( ( ) ) ( ( ) ) 3 Asst.Prof.Dr. Emre AKIN