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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.

left-half-side-member-diagrams

type-1

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

 type-2

At point 1

type-3

Verification. Equilibrium of Moments at Point 2.

type-4

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

type-5

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

equilibrium-result

Local Axis x':

type-6

Loxal Axis y':

type-7

Equilibrium of Moments at Point 1:

type-8

From the equilibrium of the part 1S – 2J

equilibrium-result-2

Local Axis x':

type-9

Loxal Axis y':

type-10

Equilibrium of forces at Point 2:

equilibrium-result-3

Local Axis x':

type-12

Loxal Axis y':

type-13

Equilibrium of Moments at Point 2:

type-14

Equilibrium of forces of the part 2S – 3J

equilibrium-result-4

Local Axis x':

type-15

Loxal Axis y':

type-16

Equilibrium of Moments at Joint 3:

type-17

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.  

axial-force-member-diagram

shear-force-member-diagram

bending-moment-member-diagram

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

type-18

This is where Moment has max value

type-19

 

 

 

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