Bending moments diagram at T intersection

In summary, for the given homework problem, the student needs to draw axial force, shear force, and bending moment diagrams, indicating the maximum and minimum values. The student has worked out the values for points A-B and B-D, but is unsure how to approach the T intersection at point D. The section DE can be treated as a cantilever and the values for the shear and moment at that section can be calculated by including the 10 kN force in the free body diagram. The FBD for DF is similar to that of AB with different values.
  • #1
mackhina
8
0

Homework Statement



Draw the axial force, shear force and bending moment diagrams. Show the locations and magnitude of the maximum and minimum values.

Homework Equations



See diagram.

The Attempt at a Solution



I've worked out the values from points A-B and then from points B-D. I don't grasp how I am suppose to approach the T intersection at point D. Should I evaluate it from D-E and treat the post from D-F as a pin joint, with values of 36.13kN and 15.13kN?

Then do the joint D-F after? If the D-E sections wasn't there I would just continue working around from D-F next, but because it is I'm not sure of how to work it out?

Any help would be heaps appreciated. Thanks a lot!

Cheers
 

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  • #2
Section DE is just a cantilever. If you cut a section thru DE in a FBD that includes the 10 kN force, the shear and moment at that section are easily calculated (no axial force). In DF, your FBD is similar to that of AB ( but with different values).
 

1. What is a bending moment diagram at T intersection?

A bending moment diagram at T intersection is a graphical representation of the internal forces acting on a structural member at a T-shaped junction. It shows the variation of bending moment along the length of the member, which is essential in determining the structural strength and stability.

2. How is a bending moment diagram at T intersection calculated?

The bending moment at any point on the member is calculated by multiplying the force acting on the member by the perpendicular distance from that point to the line of action of the force. This process is repeated for multiple points along the member, and the results are plotted on the diagram.

3. What are the key features of a bending moment diagram at T intersection?

The key features of a bending moment diagram at T intersection include the maximum positive and negative bending moments, the point of zero bending moment, and the location of the point of contraflexure (where the bending moment changes from positive to negative or vice versa).

4. How does a bending moment diagram at T intersection affect the design of a structure?

A bending moment diagram at T intersection is crucial in determining the required size and strength of structural members to withstand the internal forces and maintain stability. Designers and engineers use the diagram to select appropriate materials and dimensions for the structure.

5. Are there any limitations to using a bending moment diagram at T intersection?

While a bending moment diagram at T intersection provides valuable information for structural design, it does not take into account other factors such as shear forces, torsion, and dynamic loads. Therefore, it should be used in conjunction with other analysis methods for a comprehensive understanding of the structural behavior.

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