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Thursday, 04 February 2016 13:18cat

Calculation Example - Calculate the member diagrams

Written by  TheStructuralEngineer.info

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 1J – 1S (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 1S – 2J

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 2S – 3J

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

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