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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

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