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

[spn]

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

 

[PhanthomJay]

At points 1 and 2, what is represented by those lines with the circles at the top and bottom?

 

[spn]

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?

 

[PhanthomJay]

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.

 

[spn]

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