Need help with a Statically Indeterminate System

AI Thread Summary
The discussion focuses on solving a statically indeterminate system involving three steel bars connected to a rigid member K. The user is attempting to determine the forces in each bar and their corresponding elongations using the formula δ = (PL) / (AE). They have derived equations based on moments and force balances but are struggling with the relationships between the points of connection on the rigid member. The complexity arises from the lack of a fixed point, complicating the calculations for elongation ratios. The user seeks guidance on how to proceed with the analysis.
TA1068
Messages
13
Reaction score
0

Homework Statement



Three steel bars are pin-connected to a rigid member K. Determine the force developed in each bar. Determine the load carried be each of the tension members and the elongation of each member

http://img3.imageshack.us/img3/6850/problemdiagram.jpg

Known:
A_A_B = 0.10 in^2
E_A_B = 30E6 psi
A_C_D = 0.20 in^2
E_C_D = 15E6 psi
A_F_H = 0.30 in^2
E_F_H = 10E6 psi


Homework Equations



\delta = (PL) / (AE)


The Attempt at a Solution



Finding the moment about B:
10P_C_D + 20P_F_H = 15(15000)
or
P_F_H = 7500 - (1/3)P_C_D

The equation \delta = (PL) / (AE) yields:
P_A_B = 150,000\delta_A_B
P_C_D = 200,000\delta_C_D
P_F_H = 300,000\delta_F_H

And the sum of forces in the Y direction gives:
P_A_B + P_C_D + P_F_H = 15000


This is where I'm stuck. If any point along K was fixed it would be easy; K is rigid, so then the distance from the fixed point can be turned into a ratio to find the other \delta values. I think all 3 points (B, D, and H) are pulled downward, but I'm not sure what there relation is to each other. Any clues?
 
Last edited by a moderator:
Physics news on Phys.org
Yikes, I think my TEX tags are all messed up. Not sure how to fix it, let me know if you have any questions!
 
Now if it was something like this:
http://img194.imageshack.us/img194/8167/fixedpoint.jpg
I would say sigma_CD = 10(theta) and sigma_FH = 30(theta) and all would be good.


But since it's like this:
http://img199.imageshack.us/img199/9023/nonfixedpoint.jpg
I have another variable in there with x. Now sigma_AB = (x)(theta), sigma_CD = (10+x)(theta), and sigma_FH = (30+x)(theta)

Hmm...
 
Last edited by a moderator:

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Help understanding statically determinate/indeterminate structures
Replies
3
Views
5K
An introduction to the analysis of statically indeterminate systems
Replies
8
Views
34K

Hot Threads

Recent Insights

Back
Top