Resolving forces using Compatibility of Displacements?

Click For Summary
SUMMARY

The discussion centers on resolving forces in a pin-jointed frame subjected to a 50kN load at point A. The calculated forces in the rods are FA→C = 21.7kN, FA→B = FA→D = 16.6kN, as provided by the tutor. However, a participant claims to have calculated FA→C as 25.6kN, indicating a potential error in their approach. The equations used, particularly FA→B = FA→D = FA→C * cos(30)^2, are based on principles of static equilibrium and compatibility of displacements.

PREREQUISITES
  • Understanding of static equilibrium principles in structural analysis
  • Familiarity with compatibility of displacements in mechanics
  • Knowledge of trigonometric functions, specifically cosine
  • Proficiency in using Young's Modulus for material properties (E = 200kN/mm²)
NEXT STEPS
  • Review the derivation of force equations in pin-jointed frames
  • Study the application of compatibility of displacements in structural mechanics
  • Learn about the effects of load distribution on deflection in beams
  • Explore advanced topics in structural analysis, such as finite element methods
USEFUL FOR

Students in civil or mechanical engineering, structural analysts, and anyone involved in the design and analysis of pin-jointed frames and load-bearing structures.

mm391
Messages
65
Reaction score
0

Homework Statement



A pin-jointed frame (diagram attached) is formed of steel rods of 10mm diameter with member AC being 2m long. If a load of 50kN is applied at A as shown, determine the deflection of A and the force in the three rods. Take E = 200kN/mm^2.

Homework Equations



FA→B = FA→D = FA→C* cos(30)^2

FA→C +2*FA→B cos(30) = 50kN

The Attempt at a Solution



Our tutor has given the answers as:

FA→C = 21.7kN
FA→B=FA→D=16.6kN
And he has said FA→C = 50kN/1+2cos(30)^3)

But when I solve the equations in for FA→C I actually get= 25.6kN. can anyone help me find my error?
 

Attachments

  • Untitled1.jpg
    Untitled1.jpg
    24.4 KB · Views: 495
Last edited:
Physics news on Phys.org
If you could show your working, you would get more help. Meanwhile, on what principles are the equations "FA→B = FA→D = FA→C* cos(30)^2" based?
At what point in your calculations has the compatibility of the displacements been made?
 

Similar threads

Forces and Moments: Solving Homework Equations
  • · Replies 2 ·
Replies
2
Views
3K
How to find the forces in a particular framework of light rods
  • · Replies 11 ·
Replies
11
Views
2K
Tetrahedron with 3 points fixed, and force applied to 4th
  • · Replies 11 ·
Replies
11
Views
2K
Block on an incline and frictional force
  • · Replies 9 ·
Replies
9
Views
14K
2 unknown Forces+known resultant force
  • · Replies 1 ·
Replies
1
Views
2K
Calculating Unknown Forces in a Vector Diagram
  • · Replies 1 ·
Replies
1
Views
3K
Determine the magnitude of force at pin A as a function of position d.
  • · Replies 1 ·
Replies
1
Views
3K
Reaction Forces at Points A and B
  • · Replies 13 ·
Replies
13
Views
5K
Engineering Two approaches in statics not adding up
  • · Replies 5 ·
Replies
5
Views
2K
Three forces on a box in different directions what is the acceleration
  • · Replies 3 ·
Replies
3
Views
2K