The solid 30-mm diameter steel [E = 200 GPa] shaft shown in Figure P10.65 supports two belt
pulleys. Assume that the bearing at B can be idealized as a roller support and that the bearing at
D can be idealized as a pin support. For the loading shown, determine (a) the shaft deflection at
pulley the shaft deflection at pulley C.
Solution
We can apply Macaulays method to find the value of deflection.
But before that we have to calculate the value of reaction at B and D by applying the
equilibrium condition.
RB = 1394.44 N and the RD = 305.56 N.
Now we can apply the Macaulays method i.e.
------(1) where M is moment of the beam about the section x-x which is taken at the right of the
beam as shown in the fig.
Now we will write the equation of moment.
Mx-x = -700(X+0.5) +RAX - 1000(X-0.9)
Now we will put this in equation 1.
EI d2Y/dX2 = -700(X+0.5) +RAX - 1000(X-0.9)
NOw we will integrate this equation and it become
We will integrate this once again and it will becomes
-----(A)
NOw we will put the initial condition that is at X = 0 , Y = 0 and at X = 1.8 Y = 0.
By applying these condition we will get the value of Constants .
Then by putting the value of X in the final equation (A) we can get the value of deflection..
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
The solid 30-mm diameter steel [E = 200 GPa] shaft shown in Figure P.pdf
1. The solid 30-mm diameter steel [E = 200 GPa] shaft shown in Figure P10.65 supports two belt
pulleys. Assume that the bearing at B can be idealized as a roller support and that the bearing at
D can be idealized as a pin support. For the loading shown, determine (a) the shaft deflection at
pulley the shaft deflection at pulley C.
Solution
We can apply Macaulays method to find the value of deflection.
But before that we have to calculate the value of reaction at B and D by applying the
equilibrium condition.
RB = 1394.44 N and the RD = 305.56 N.
Now we can apply the Macaulays method i.e.
------(1) where M is moment of the beam about the section x-x which is taken at the right of the
beam as shown in the fig.
Now we will write the equation of moment.
Mx-x = -700(X+0.5) +RAX - 1000(X-0.9)
Now we will put this in equation 1.
EI d2Y/dX2 = -700(X+0.5) +RAX - 1000(X-0.9)
NOw we will integrate this equation and it become
We will integrate this once again and it will becomes
-----(A)
NOw we will put the initial condition that is at X = 0 , Y = 0 and at X = 1.8 Y = 0.
By applying these condition we will get the value of Constants .
Then by putting the value of X in the final equation (A) we can get the value of deflection.
![The solid 30-mm diameter steel [E = 200 GPa] shaft shown in Figure P10.65 supports two belt
pulleys. Assume that the bearing at B can be idealized as a roller support and that the bearing at
D can be idealized as a pin support. For the loading shown, determine (a) the shaft deflection at
pulley the shaft deflection at pulley C.
Solution
We can apply Macaulays method to find the value of deflection.
But before that we have to calculate the value of reaction at B and D by applying the
equilibrium condition.
RB = 1394.44 N and the RD = 305.56 N.
Now we can apply the Macaulays method i.e.
------(1) where M is moment of the beam about the section x-x which is taken at the right of the
beam as shown in the fig.
Now we will write the equation of moment.
Mx-x = -700(X+0.5) +RAX - 1000(X-0.9)
Now we will put this in equation 1.
EI d2Y/dX2 = -700(X+0.5) +RAX - 1000(X-0.9)
NOw we will integrate this equation and it become
We will integrate this once again and it will becomes
-----(A)
NOw we will put the initial condition that is at X = 0 , Y = 0 and at X = 1.8 Y = 0.
By applying these condition we will get the value of Constants .
Then by putting the value of X in the final equation (A) we can get the value of deflection.](https://image.slidesharecdn.com/thesolid30-mmdiametersteele200gpashaftshowninfigurep-230327025336-23fef83d/85/The-solid-30-mm-diameter-steel-E-200-GPa-shaft-shown-in-Figure-P-pdf-1-320.jpg)
