Calculation Example - Calculate the member diagrams

Calculate the member diagrams for Axial Force N, Shear Force S and bending Moment M for the following frame.

Solution

 

The frame is symmetrical in shape, loading and constraints. So we can work on the left half side.

At point 3 there is no moment because it is a hinge.

 

At point 1

Verification. Equilibrium of Moments at Point 2.

The trigonometrical numbers for angles ?1, ?2 (units degrees) are

The equilibrium of the part 1^J – 1^S (where the upper script J means Joint and S means Section) gives:

Local Axis x^':

Loxal Axis y^':

Equilibrium of Moments at Point 1:

From the equilibrium of the part 1^S – 2^J

Local Axis x^':

Loxal Axis y^':

Equilibrium of forces at Point 2:

Local Axis x^':

Loxal Axis y^':

Equilibrium of Moments at Point 2:

Equilibrium of forces of the part 2^S – 3^J

Local Axis x^':

Loxal Axis y^':

Equilibrium of Moments at Joint 3:

With the above values we make the diagrams for the Axial Force N, Shear Force S and Bending Moment at the members of the left part 1-2-3. Because of symmetry we can have diagrams for the right part 3-4-5. Diagrams for Axial Force and Moment are symmetric and diagram for Shear is antisymmetric.  

The Shear diagram takes zero value at distance x from Joint 2

This is where Moment has max value