Solve Indeterminate Beam using Force Method: Step-by-Step Guide | Homework Help

In summary, you need to use the Force method of analysis to determine the redundant forces on a triple propped cantilever beam, and then use the equations for the beam to solve for the unknowns.
  • #1
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Homework Statement


I need help starting with this question.. I am very confused because the lecturer gave examples when its a canteleaver beam but not when it is in supported structure. I

For the given beam (Table 1, Figure 1):
• determine the number of degrees of freedom to which the
beam is indeterminate
• use Force Method of Analysis to determine the redundant
force(s)
• sketch the Free Body Diagram (FBD)
• construct the Shear Force Diagram (SFD) and the Bending
Moment Diagram (BMD)
• define dimensions for the cross section of the I-beam by
using the Main Strength Condition
• determine the deflection (or the slope) at a point A.
Take [ ] 160MPa; E 200 GPa; a 1m






Homework Equations



wont require yet as i just need help to set up the FBD

The Attempt at a Solution


I just needs step on how to set up using the Force method... Please view my attempt and comment if i am correct or wrong...

img.photobucket.com/albums/v236/ilmman/Ass2attempt1.jpg

img.photobucket.com/albums/v236/ilmman/Ass2attempt2.jpg
 
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  • #2
At points 1 and 2, what is represented by those lines with the circles at the top and bottom?
 
  • #3
PhanthomJay said:
At points 1 and 2, what is represented by those lines with the circles at the top and bottom?

those are supposed to be supported beams... the circles are hinges. Using the 3L - H I got 3(2)-3 = 3 ... Indeterminates... I have to make it determinate by adding redundant forces which i have attempted from the links above. Can someone please confirm if it is correct?
 
  • #4
So it looks like you've got a triple propped cantilever beam, that is fixed at one end and pinned or hinged supported at three other locations along the beam, with an applied force and applied couple and applied uniform load. Thus, you have 5 unknown support reactions (4 vertical forces at the 4 reaction points, plus a couple at the fixed end, = 5), and just 2 equilibrium equations (sum of y forces =0 and sum of momemts about any point = 0), so the beam is statically indeterminate to the 3rd degree. Your free body diagram is therefore correct. Now you must solve for the unknowns. I am also assuming that those hinged beam reactions X1 and X2 are near rigid, that is, they are similar to a pinned support such as you have at X3, such that the vertical deflections at points 1, 2, and 3, as well as at the fixed end, are 0. Otherwise, if the beam supports are flexible ('springy'), you've got yourself a problem. That's why I asked what the symbols represented.
 
  • #5
PhanthomJay said:
So it looks like you've got a triple propped cantilever beam, that is fixed at one end and pinned or hinged supported at three other locations along the beam, with an applied force and applied couple and applied uniform load. Thus, you have 5 unknown support reactions (4 vertical forces at the 4 reaction points, plus a couple at the fixed end, = 5), and just 2 equilibrium equations (sum of y forces =0 and sum of momemts about any point = 0), so the beam is statically indeterminate to the 3rd degree. Your free body diagram is therefore correct. Now you must solve for the unknowns. I am also assuming that those hinged beam reactions X1 and X2 are near rigid, that is, they are similar to a pinned support such as you have at X3, such that the vertical deflections at points 1, 2, and 3, as well as at the fixed end, are 0. Otherwise, if the beam supports are flexible ('springy'), you've got yourself a problem. That's why I asked what the symbols represented.


Thanks for the help. Unfortunately My Supported reactions were screwed up and I did it completely wrong, the correct proceedure was to keep the PIN and replace one of the other support reactions with a redundant foce, so I can make it determinate (Using 3L - H I got 1 meaning I should have 1 indeterminate force). Your knowledge seem too far ahead as I haven't gone up to third degree yet :P thank you anyways for helping me
 

What is the force method?

The force method is a structural analysis technique used to determine the internal forces and displacements of a structure. It is based on the principles of equilibrium and compatibility, and is commonly used in the design of structural systems.

How does the force method differ from the displacement method?

The force method differs from the displacement method in that it considers the internal forces and stresses of a structure, rather than just the displacements. It is also more suitable for analyzing indeterminate structures, as it does not require the use of compatibility equations.

What are the basic steps of the force method?

The basic steps of the force method include: 1) Determining the number of unknown forces and displacements, 2) Establishing a set of independent equilibrium equations, 3) Solving for the unknown forces using the equilibrium equations, 4) Calculating the reactions and internal forces, and 5) Checking the compatibility of the displacements.

What are the advantages of using the force method?

There are several advantages of using the force method, including: 1) It can be used to solve indeterminate structures, 2) It provides a more accurate analysis of the internal forces and stresses, 3) It is easier to use for complex structures, and 4) It can be used to determine the stiffness of a structure.

What are the limitations of the force method?

The force method has a few limitations, including: 1) It cannot be used for structures with large nonlinear deformations, 2) It does not take into account the effects of material properties, such as stiffness and ductility, and 3) It cannot be used to analyze structures with large displacements or rotations.

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