The 80-mm-diameter solid shaft is subjected to the distributed and concentrated torsional loadings shown, where T = 500 N-m. (Figure 1)
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Determine the shear stress at point A and point B with appropriate units
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- A full quarter-circular fillet is used at the shoulder of a stepped shaft having diameter D2= 1.0 in. (see figure), A torque T = 500 lb-in. acts on the shaft. Determine the shear stress at the stress concentration for values as follows: D1= 0.7,0.8, and 0.9 in. Plot a graph showing versus D?complete solution A solid steel shaft must not twist through more than 30 in a 6-m length whented to a torque of 12 kN • m. (a) Find the diameter of the smallest shaft thatcan be used. (b) What is the maximum shear stress in the shaft of this diameter? UseG = 83 GPa for steel.The 46-mm diameter shaft is supported by a smooth thrust bearing at A and a smooth journal bearing at B. The pulleys C and D are subjected to the vertical and horizontal loadings shown in the figure below. (Figure 1)
- A alm T 1.20 m T B 1.20 m C 3 T The 60 mm diameter shaft is made of 6061-T6 aluminum having an allowable shear stress of Tallow 80 MPa. Find the corresponding angle of twist of disk A relative to disk C. Note: You will need to calculate the maximum allowable torque T first. Provide your answer for angle of twist in radians with 3 significant figures after the decimal point.2. Solve the following problem Two designs for a shaft are being considered. Both have an outside diameter of 70 m and are 900 mm long. One is solid but the other is hollow with an internal diameter of 50 mm. Both are made from steel (G=120 GPa). Critically evaluate and compare the torsional shear stress, angle of twist of the two designs if they are subjected to a torque ofT 171N.m the missing Torque 171(T).The rotating solid steel shaft is simply supported by bearings at points B and C and is driven by a gear (not shown) which meshes with the spur gear at D, which 250 mm has a 150 mm pitch diameter. The force F from the drive gear acts at a pressure angle of 20°. The shaft transmits a torque to point A of T = 340 N. m. The shaft 100 mm is machined from steel with S, = 420 MPa. Using a factor of safety of 2.5, determine the minimum allowable diameter of the 250 mm section of the shaft based on a static yield analysis using the distortion energy theory and maximum shear stress theory.
- Determine the minimum diameter that can be used for a solid circular steel shaft which is limited to an allowable shear stress of 70 MPa and a maximum angle of twist of 1.5o (degrees) per meter length. Applied maximum torque is 25 KN-m and the overall shaft length is 1.25 meters. Shear modulus = G= 80 GPa Note: When using torsion stress formulas, you must convert the angle of twist from degrees to radians.A solid shaft BC is fixed at the B end and subjected to torque T at the C end, as shown below. The shaft remains elastic and has shear modulus G. Which expression below represents the angle of rotation at the C end? radius R T B (It will be easier to use Castigliano's theorem.)The end of a 2.5 in diameter steel shaft is milled to two flats (one flat on the top and one flat at the bottom) to permit the use of a hand crank. Each flat is located 1.00 in from the center of the shaft. A torque of 750 Ib-in is applied. Find: (a) the maximum shear stress at the end of the shaft with two flats in psi unit. (b) the angle of twist in fadians (c) the angle of twist in degrees h= 1.0 in h= 1.0 in d= 2.50 in Show all your calculations.
- The rotating solid steel shaft is simply supported by bearings at points B and C and is driven by a gear (not shown) which meshes with the spur gear at D, which has a 140-mm pitch diameter. The force F from the drive gear acts at a pressure angle of 20°. The shaft transmits a torque to point A of TA = 260 N-m. The shaft is machined from steel with Sy = 400 MPa and Sut = 560 MPa. Assume factor of safety and all other factors as (one) 1,. Determine the minimum allowable diameter of the 100-mm section of the shaft for infinite life (selectec criter sould be written at the begining of the solution) 250 mm 100 mm 20Design a hallow shaft (Diameter and length) that develops 80 kN of power while rotating at a speed of 4000 rpm. The design constrains are as under: The angle of twist not to exceed 0.200 Shear stress is not to exceed 480 MN/m? The outer diameter is to be twice the inner diameter. The shaft length is to be three times the outer diameter. Modulus of rigidity = 79 GN/m?.A shaft has an external diameter (ED) of 350 mm and an internal diameter of 150 mm. i. Calculate the maximum shear stress in the shaft when it is transmitting 3700 kW at 100 rpm. ii. Find the angle of twist in a length of 20 x ED. (Assume G=75GN/m2). iii. If the hollow shaft is replaced by a solid shaft of the same weight and length, what power can it transmit for the same maximum shear stress?