Resolving forces using Compatibility of Displacements?

In summary, a pin-jointed frame made of steel rods is under a load of 50kN at point A. The deflection at A and the forces in the three rods are being determined, with a known length and modulus of elasticity. The tutor has given answers for the forces, but the student has found a different result when solving for FA→C. The student is seeking help to find their error and is asked to show their working and explain the principles behind the equations. The compatibility of displacements has not been addressed in the calculations.
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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?
 

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  • #2
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?
 

What is "Resolving forces using Compatibility of Displacements?"

"Resolving forces using Compatibility of Displacements" is a method used in mechanics to find the unknown forces acting on a system by analyzing the displacement compatibility of the system.

Why is "Resolving forces using Compatibility of Displacements" important?

This method is important because it allows us to determine the forces acting on a system without directly measuring them. This can be useful in situations where direct measurement is not possible or practical.

What are the steps involved in "Resolving forces using Compatibility of Displacements"?

The steps involved in this method are: 1) drawing a free body diagram of the system, 2) applying the principle of virtual work to the system, 3) writing the compatibility equations, 4) solving the equations to find the unknown forces.

What are some common applications of "Resolving forces using Compatibility of Displacements"?

This method is commonly used in structural analysis, such as determining the forces in trusses and frames. It is also used in other fields such as civil engineering, aerospace engineering, and biomechanics.

Are there any limitations to "Resolving forces using Compatibility of Displacements"?

Yes, this method assumes that the system is in static equilibrium and that the materials involved are linearly elastic. It may not be applicable in situations where there are non-linear materials or dynamic forces at play.

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