Deflection Question

[MatthewMansfield]

Hello all

I was hoping someone could help with the following:-

I have a pin jointed truss (all members are joined by frictionless pins and load is only applied to the joints), supported by 2 x pin jointed supports.

If my pin jointed structure was loaded solely at a joint with 200kN which resulted in a vertical deflection of 22mm with a Youngs modulus of 150kN/mm^2.

If I then doubled the load to 400kN but kept everything else the same then what would happen to my deflection?

I think the vertical deflection will double from 22mm to 44mm - but how can I prove this with without detailed calculations?

I know that if I halved the young's modulus then this would be result in the deflection doubling.

Is there any other ways of proving that the deflection will double (assuming it does double)???

Thank you.

 

[MegaStructures]

If the structure is in the linear range (no yielding occurs) your assumption is correct. Matrix structural analysis says deflection equals force divided by structures stiffness (F=K*x). The stiffness of the structure does not change with force in the linear range; therefore, deflection increases proportionately with force.

“The most successful people in life are the ones who ask questions. They’re always learning. They’re always growing. They’re always pushing.” Robert Kiyosaki

 

[JStephen]

I'm not sure of your support conditions. I'm visualizing a 2D truss with one end pinned and one free to slide, so the whole arrangement works like a simply supported beam.
First off, you can go through and show that each member force is proportional to the applied load. This can be shown fairly easily, F1 = (F2 sin(theta2) + F3 sin (theta3))/Sin (theta1), etc. and without solving for any particular force, you can show they are proportional to the applied force.
And for a pinned truss, that means the longitudinal deflection in each member is proportional to the applied load.
So you can show all of the individual forces and individual axial deflections are proportional to the applied force.
Then set the sum of the work or energy put into the system by the applied force equal to the sum of the energies put into each individual member. This will show that the overall deflection at the applied load must be proportional to the load as well, which is what you need.
Now, in this approach, one assumption is that deflections are small enough that geometry and the angles of the members do not change significantly. For a typical bridge-type truss that's probably a pretty good assumption.
If you take a series of members pinned together, without the truss, pin both ends, and apply a lateral force, you get a catenary-type effect even without the truss, and in that case, the deflection is not necessarily proportional to the force. I'm assuming that effect is not affecting your truss.

 

[MegaStructures]

JStephen I think your approach is entirely unnecessary. F=k*x works at the member and structure level for linear material reactions and small deformations. It’s acceptable to say deflection is linearly proportional to force given those assumptions are true

“The most successful people in life are the ones who ask questions. They’re always learning. They’re always growing. They’re always pushing.” Robert Kiyosaki

 

[rb1957]

is your structure determinate ? (I think I know the answer, I'm trying to give you questions to ask yourself to solve your question)

if you "know" that 1/2 the stiffness doubles the deflection, then doubling the load should ... double the deflection.

another day in paradise, or is paradise one day closer ?

 

[JStephen]

Mega- the poster didn't ask if F=Kx works for the overall structure, they asked how you prove it, which is a different problem.

 

[engineering_patrol]

Yes, it will double, as linearity is the most basic concept of static analysis of first order.

 

[BridgeSmith]

Sounds like a homework problem to me. No such thing as "frictionless pins" in the real world. Also, in the real world there's always movement at the joints, non-linear stiffness, etc. I thought we had a student area for this type of query.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[phamENG]

BridgeSmith - Mr. Mansfield frequently posts these highly theoretical/hypothetical questions. If you check his profile, he's been around for 9 years. I made the mistake of calling him out as a student a on the Civil forum a few months ago.

 

[BridgeSmith]

BridgeSmith - Mr. Mansfield frequently posts these highly theoretical/hypothetical questions. If you check his profile, he's been around for 9 years. I made the mistake of calling him out as a student a on the Civil forum a few months ago.

Good to know, I guess. I don't see the point of asking those "highly theoretical/hypothetical questions", though. I would think most of us have enough real problems we have to find solutions for.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[Tomfh]

Aside from non linearity and second order effects, yes the deflection will double. Why wouldn’t it?

Doubling the load will have the same effect on member strain (and hence overall deflection) as halving the elastic modulus.