Question 3

Shaft AE is supported by journal bearings at A, C and E. The intermediate support C sits on the I-section beam FG. The shaft supports two pulley loads at B and D. Determine the reaction forces at A, C and E.

Question 3

Question 3

Step 1:
Identify redundant supports and setup compability equation

Step 1:
Identify redundant supports and setup compability equation

Step 2:
Obtain expressions for each displacement in the compability equation

Step 2:
Obtain expressions for each displacement in the compability equation

Step 3:
Solve for reactions at A, C and E

Step 3:
Solve for reactions at A, C and E

Useful formula:

Useful formula:

Virtual work working to get Δ_Ci

Virtual work working to get Δ_Ci

Step 1:
Obtain internal bending moments due to real load

Step 1:
Obtain internal bending moments due to real load

Step 2:
Obtain internal bending moments due to virtual load

Step 2:
Obtain internal bending moments due to virtual load

Step 3:
Use virtual work formula to find Δ_Ci

Step 3:
Use virtual work formula to find Δ_Ci

Useful formula:

Useful formula:

Question 3

Question 3

Step 1: Identify redundant supports and setup compability equation Step 1: Identify redundant supports and setup compability equation

Step 2: Obtain expressions for each displacement in the compability equation Step 2: Obtain expressions for each displacement in the compability equation

Step 3: Solve for reactions at A, C and E Step 3: Solve for reactions at A, C and E

Useful formula: Useful formula:

Virtual work working to get ΔCi

Virtual work working to get ΔCi

Step 1: Obtain internal bending moments due to real load Step 1: Obtain internal bending moments due to real load

Step 2: Obtain internal bending moments due to virtual load Step 2: Obtain internal bending moments due to virtual load

Step 3: Use virtual work formula to find ΔCi Step 3: Use virtual work formula to find ΔCi

Useful formula: Useful formula:

Step 1:
Identify redundant supports and setup compability equation

Step 1:
Identify redundant supports and setup compability equation

Step 2:
Obtain expressions for each displacement in the compability equation

Step 2:
Obtain expressions for each displacement in the compability equation

Step 3:
Solve for reactions at A, C and E

Step 3:
Solve for reactions at A, C and E

Useful formula:

Useful formula:

Virtual work working to get Δ_Ci

Virtual work working to get Δ_Ci

Step 1:
Obtain internal bending moments due to real load

Step 1:
Obtain internal bending moments due to real load

Step 2:
Obtain internal bending moments due to virtual load

Step 2:
Obtain internal bending moments due to virtual load

Step 3:
Use virtual work formula to find Δ_Ci

Step 3:
Use virtual work formula to find Δ_Ci

Useful formula:

Useful formula: