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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 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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