Engineering problem on lateral force to a simple portal frame

[SamuelGompers]

Homework Statement

A single story single bay building model has fixed fixed columns and a rigid beam. the total length of each aluminum column is 24 in. tall by 4 in wide and 32/1000 in thick. the plexiglas beams used for the base and top story are 12 in wide 4 in deep and .5 in thick.

a. Determine the lateral stiffness

b. Determine the maximum load V that can be applied at the top of the frame so that the columns do not yield

c. What is the corresponding deflection that the frame can withstand

Homework Equations

k=(12EI)/L³
I=(bh³)/12
σ=33 ksi
σ=(M(thickness/2))/I
M=V(x)-V(L/2)
E=10.4x10⁶ psi

The Attempt at a Solution

I=1.09x10^-5 in.⁴
k=.197 lb/in.
so this is the answer to a.
M=22.48 per beam
so total M_{T[/SUB=45 lb in.
V=3.74 lb
so this is the answer to b
Δ=20.95 in
answer to c}

 

[KataKoniK]

Thank you for your post. I would like to offer some feedback on your solution attempt.

Firstly, for part a, it would be helpful to include the units for the lateral stiffness (k). It appears that you have calculated it in units of lb/in, which is correct. Additionally, it would be helpful to include the total length of the columns (L) in your calculation, as it is necessary for the formula you have used.

For part b, it is important to clarify what you mean by "per beam." Are you referring to the maximum bending moment on each beam, or the total bending moment on all beams? Additionally, it would be helpful to see your calculations for determining the maximum load (V) that can be applied at the top of the frame without yielding.

For part c, the units for deflection (Δ) should be in inches, not in. Additionally, it would be helpful to see your calculations for determining the corresponding deflection that the frame can withstand.

Overall, it appears that you have used the correct formulas and units in your solution attempt. However, it would be helpful to provide more detailed and organized calculations to fully support your answers. It is also important to clearly define any variables or terms that you use in your calculations. I hope this feedback helps you in your problem-solving process. Good luck!