Assume a solid shaft with a diameter of d, and the load at the end is...
Assume a solid shaft with a diameter of d, and the load at the end is P. Use Castigliano's method, find the linear deflection and the angular deflection from bending at the suspending end of the shaft , and the angular deflection from Torsion. In terms of P,T,d and the Modulus E and G.
1) Energy equation
2)linear deflection
3) Angular deflection from bending
4) Angular deflection from torsion
Homework Answers
Castigliano's theorem relates strain energy to angular and linear deflection. Strain energy is first calculated for the given case and then linear and angular deflections are calculated with the help of Castigliano's method.
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Assume a solid shaft with a diameter of d, and the load at the
end is...
3. Power transmission is an important engineering application and relies on the integrity of the shaft designs. Assume a solid, circular steel shaft with a uniform diameter d 50 mm and a total le...
3. Power transmission is an important engineering application and relies on the integrity of the shaft designs. Assume a solid, circular steel shaft with a uniform diameter d 50 mm and a total length I3 m. At its midpoint, a belt passes over a pulley and delivers 50 kW power to the shaft. This power is used to drive two machines at either end of the shaft. Machine 1 consumes P1 20 kW and machine 2 uses P230 KW. The...
design a shaft to transmit a load based on B106.1 which is attached Design a shaft...
design a shaft to transmit a load based on B106.1 which is
attached
Design a shaft to transmit a load based on ANSI/ASME Standard B106.IM-1985 (40 points) a) Identify which loading case this analysis can be applied to and why: Case i) T. -9 kNm, T, -0,M.-0, M.-6.5 kNm, kr 1.57, n = 2 Case ii) T. - 7 kNm, T.-0, M -8 kNm, M-6 kNm, k-1.57, n-2 b) Perform the design and calculation on the acceptable case with: i)...
Questions must be answered in the space provided 6. You must show your work to obtain full credit 1. (50 points) Determine the maximum deflections in torsion and in bending of the shaft shown in...
Questions must be answered in the space provided 6. You must show your work to obtain full credit 1. (50 points) Determine the maximum deflections in torsion and in bending of the shaft shown in a. Figure for the data given below if the steel shaft diameter is 2 in Shaft length L 25 in Applied load P- 1300 lbf Maximum torque Tmax= 2500 lbfin Distance to Pb- 20 in Distance between bearings a -16i Young's modulus E-30x lof psi...
Question: Analyse the efficiency of transmitting power using a solid shaft of diameter "d" compared to...
Question: Analyse the efficiency of transmitting power using a solid shaft of diameter "d" compared to a hollow shaft of diameters "Do" and "Di". The ratio "r" = Do/Di should be varied from 1.5, 1.6, 1.7, 1.8; 1.9; and 2.0 but the weight of the hollow shaft must be equal to the weight of the solid shaft. Assume the length of the shaft between the two bearings (see figure below) to be the same. must be until you find the...
A vertical load P = 150 kN is applied to a circular solid shaft which in turn is supported by a circular end cap as sho...
A vertical load P = 150 kN is applied to a circular solid shaft which in turn is supported by a circular end cap as shown below. Both members are made of steel with allowable normal stress = 160 MPa, allowable shear stress 100 MPa, and allowable bearing stress 200 MPa. Determine the minimum required diameter of the solid shaft, and the minimum required outer diameter and thickness of the circular end plate. P 150 kN ds d 30 mm...
+ A cantilever beam with a round cross section has a concentrated load F at the...
+ A cantilever beam with a round cross section has a concentrated load F at the end. The total strain energy due to bending and direct shear is given as: F/1.11F1 U=- 6EI 2 AG Using Castigliano's method find the total deflection at the free end in inches. ned" nad Given that I = -, G=12 Mpsi, F=150 lbf, I=12 in, E =31 Mpsi, and d=1.25 in. 64 Hint: y = OU OF
(30 pts) Shaft Yielding. A solid circular shaft with 125 mm diameter rotates in bearings at 30 rad/s. Transverse loadings produce a maximum bending moment of 10 kNm. (For 3. e meaning of transver...
(30 pts) Shaft Yielding. A solid circular shaft with 125 mm diameter rotates in bearings at 30 rad/s. Transverse loadings produce a maximum bending moment of 10 kNm. (For 3. e meaning of transverse loading see the image below.) Given the tensile yield strength th of the shaft material as 300 MPa, find the power this shaft can transmit according to the Tresca and von Mises yield criteria. Hint: You may need to use Engineer's Theory of Bending (ETB) to...
Help Please A solid steel shaft AC is fixed to a rigid wall at its end...
Help Please
A solid steel shaft AC is fixed to a rigid wall at its end A and is connected to a solid aluminum shaft CD at its other end C. The torques Ti and Tz are applied at the sections R and D, respectively, as shown in the figure. All the dimensions are given in the figure and the weight of the shafts are neglected. The shear modulus of steel is Gst 78 GPa and the shear modulus of...
a solid circular shaft of radius a is subjected to the combined axial load P, bending moment M, and torsional moment T shown. Assume that M = Pa/2 and T = Pa/2. The axial load is constant while the m...
a solid circular shaft of radius a is subjected to the
combined axial load P, bending moment M, and torsional moment T
shown. Assume that M = Pa/2 and T = Pa/2. The axial load is
constant while the moments M and T are completely reversed cyclic
(recall, completely reversed cyclic means having the same amplitude
in positive and negative sense in a cycle). The material of the
shaft has the yield stress of 300 MPa and endurance limit of...
(b) The A-36 solid steel shaft is 3.5 m long and has a diameter of 60...
(b) The A-36 solid steel shaft is 3.5 m long and has a diameter of 60 mm. The shaft is used to transmit a torque of T = 524 N·m from the engine to the generator. Determine the angle of twist (0) of the shaft. The shear modulus of elasticity (G) of the shaft material is 75 GPa.
3. Power transmission is an important engineering application and relies on the integrity of the shaft designs. Assume a solid, circular steel shaft with a uniform diameter d 50 mm and a total length I3 m. At its midpoint, a belt passes over a pulley and delivers 50 kW power to the shaft. This power is used to drive two machines at either end of the shaft. Machine 1 consumes P1 20 kW and machine 2 uses P230 KW. The...
design a shaft to transmit a load based on B106.1 which is
attached
Design a shaft to transmit a load based on ANSI/ASME Standard B106.IM-1985 (40 points) a) Identify which loading case this analysis can be applied to and why: Case i) T. -9 kNm, T, -0,M.-0, M.-6.5 kNm, kr 1.57, n = 2 Case ii) T. - 7 kNm, T.-0, M -8 kNm, M-6 kNm, k-1.57, n-2 b) Perform the design and calculation on the acceptable case with: i)...
Questions must be answered in the space provided 6. You must show your work to obtain full credit 1. (50 points) Determine the maximum deflections in torsion and in bending of the shaft shown in a. Figure for the data given below if the steel shaft diameter is 2 in Shaft length L 25 in Applied load P- 1300 lbf Maximum torque Tmax= 2500 lbfin Distance to Pb- 20 in Distance between bearings a -16i Young's modulus E-30x lof psi...
Question: Analyse the efficiency of transmitting power using a solid shaft of diameter "d" compared to a hollow shaft of diameters "Do" and "Di". The ratio "r" = Do/Di should be varied from 1.5, 1.6, 1.7, 1.8; 1.9; and 2.0 but the weight of the hollow shaft must be equal to the weight of the solid shaft. Assume the length of the shaft between the two bearings (see figure below) to be the same. must be until you find the...
A vertical load P = 150 kN is applied to a circular solid shaft which in turn is supported by a circular end cap as shown below. Both members are made of steel with allowable normal stress = 160 MPa, allowable shear stress 100 MPa, and allowable bearing stress 200 MPa. Determine the minimum required diameter of the solid shaft, and the minimum required outer diameter and thickness of the circular end plate. P 150 kN ds d 30 mm...
+ A cantilever beam with a round cross section has a concentrated load F at the end. The total strain energy due to bending and direct shear is given as: F/1.11F1 U=- 6EI 2 AG Using Castigliano's method find the total deflection at the free end in inches. ned" nad Given that I = -, G=12 Mpsi, F=150 lbf, I=12 in, E =31 Mpsi, and d=1.25 in. 64 Hint: y = OU OF
(30 pts) Shaft Yielding. A solid circular shaft with 125 mm diameter rotates in bearings at 30 rad/s. Transverse loadings produce a maximum bending moment of 10 kNm. (For 3. e meaning of transverse loading see the image below.) Given the tensile yield strength th of the shaft material as 300 MPa, find the power this shaft can transmit according to the Tresca and von Mises yield criteria. Hint: You may need to use Engineer's Theory of Bending (ETB) to...
Help Please
A solid steel shaft AC is fixed to a rigid wall at its end A and is connected to a solid aluminum shaft CD at its other end C. The torques Ti and Tz are applied at the sections R and D, respectively, as shown in the figure. All the dimensions are given in the figure and the weight of the shafts are neglected. The shear modulus of steel is Gst 78 GPa and the shear modulus of...
a solid circular shaft of radius a is subjected to the
combined axial load P, bending moment M, and torsional moment T
shown. Assume that M = Pa/2 and T = Pa/2. The axial load is
constant while the moments M and T are completely reversed cyclic
(recall, completely reversed cyclic means having the same amplitude
in positive and negative sense in a cycle). The material of the
shaft has the yield stress of 300 MPa and endurance limit of...
(b) The A-36 solid steel shaft is 3.5 m long and has a diameter of 60 mm. The shaft is used to transmit a torque of T = 524 N·m from the engine to the generator. Determine the angle of twist (0) of the shaft. The shear modulus of elasticity (G) of the shaft material is 75 GPa.
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