Statically Indeterminate Bar with alternating area and length

Click For Summary
SUMMARY

The discussion focuses on solving a statically indeterminate bar problem with alternating area and length. The user calculated the reactions RA and RD, arriving at RA = 10.5 kN to the left and RD = 2 kN to the right. The user struggled with the algebra involving the total change in length equation, specifically the contributions from three sections of the bar. A suggestion was made to utilize a Free Body Diagram to determine the force in the middle segment, which is not simply P.

PREREQUISITES
  • Understanding of statics and force balance principles
  • Familiarity with Free Body Diagrams
  • Knowledge of material properties such as Young's Modulus (E) and cross-sectional area (A)
  • Ability to perform algebraic manipulations in structural analysis
NEXT STEPS
  • Study the principles of statically indeterminate structures
  • Learn how to create and analyze Free Body Diagrams in structural mechanics
  • Explore the concept of axial deformation in materials, focusing on Young's Modulus
  • Practice solving problems involving multiple sections of bars with varying properties
USEFUL FOR

Engineering students, structural analysts, and professionals involved in mechanical and civil engineering who are working on problems related to statically indeterminate structures.

hboyd3
Messages
1
Reaction score
0
http://img197.imageshack.us/img197/5981/probie.png

So first I did a force balance (dFx=0)

P=PB-PC=8.5kN

RD= RA - P
RA = RD + P

I know the total change in length is equal to 0, so

dAB + dBC + dCD = 0

==>

(RA*L1)/(E*A1) + (P*L2)/(E*A2) + ((RA-P)*L1)/(E*A1) = 0

but when I do the algebra I can never get it to work. my numbers never match the answer no matter which way I approach it. I can do problems with only 2 different sections but this 3 sectioned one has me baffled.

the answers are
RA= 10.5kN to the left
RD= 2kN to the right

anyone have any insight?
 
Last edited by a moderator:
Physics news on Phys.org
You are assuming that the force in the middle segment is P. It is not. Cut a section (Free Body Diagram) thru the middle bar and determine the force in that bar as a function of the known and unknown variables.
 

Similar threads

Statically Indeterminate Stepped Bar Problem
  • · Replies 5 ·
Replies
5
Views
8K
Area surface of revolution (rotating this astroid curve around the x-axis)
  • · Replies 2 ·
Replies
2
Views
2K
Platinum resistance thermometer and Kirchoff's Laws
  • · Replies 1 ·
Replies
1
Views
3K
Using Stress/Strain Curve to Find Yield Strength and Modulus of Elasticity
  • · Replies 6 ·
Replies
6
Views
88K
Change in length LSolve Engineering Problems: P, Brass, Steel
  • · Replies 1 ·
Replies
1
Views
2K
How Does Stretching a Wire Affect Its Resistance Ratio?
  • · Replies 7 ·
Replies
7
Views
7K
Solving Design Project w/ Thermal Switch (Statics)
  • · Replies 1 ·
Replies
1
Views
5K
Graduate Magnetic Field at any Point Around a Finite Straight Wire
  • · Replies 3 ·
Replies
3
Views
6K
U-Tube Fluid Statics: Solving for Water Column Length and Mercury Rise
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Some thoughts about Bell's string paradox alternatives
  • · Replies 75 ·
3
Replies
75
Views
7K