A funny statics problem 13

[NedGan76]

Hi, everyone!

Here is an interesting and funny statics problem, to exercise engineering brains and cheer up.

Given the following structure can you tell, without calculating, in which direction point A will move after deformation:
A) up
B) down
C) will not move

... and why? Point A is not a hinge. No structural analysis programs allowed.

 

[hokie66]

Down. The forces will go straight down the columns. The only deformation will be column shortening.

 

[GregLocock]

What's the constraint at the base of the right hand column?

Cheers

Greg Locock


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[hokie66]

My answer was based on it being either or pinned.

 

[NedGan76]

There is no restraint at the right hand column.

 

[IDS]

For the top pin support to balance, the shear force in the top beam must be equal at both ends, so there can be no axial force in the left-hand column.

Point A will therefore have zero deflection relative to the pinned support at the base.

But the support at the base will deflect downwards slightly, so Point A will also have an absolute downward deflection.

But the top support will deflect more than the base support, so Point A will deflect upwards relative to the top support.

So Point A moves up, and down, and does not move.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[3DDave]

"A" will deflect sideways.

 

[Tomfh]

Won’t move

 

[robyengIT]

for me point A will go up because there will be a moment in A due to that A is not a hinge, whilst the point opposite to A can rotate freely

 

[FEA way]

 

[robyengIT]

FEA : no structural program allowed, but it looks like that I am the winner. Where I have to go to withdraw the prize ?

 

[NedGan76]

FEA Way, you are not playing fair. Said no computers allowed.

But the question still remains: why is this happening like that?

Cheers!
Ned Ganchovski

A better software for your calculation notes, free and open source:

https://github.com/Proektsoftbg/Calcpad

 

[Celt83]

The rigidity of joint a combined with the horizontal restraint provided by the vertical roller at the bottom support condition behave in a similar manner to that of a top cardinal point offset. The cross-section rotation at joint a is restrained forcing rotation counter to the loading the top support is pinned so this rotation carries thru the top joint helping to drive the right point load further downward.

 

[Celt83]

 

[SE2607]

No movement.

 

[Eng16080]

The answer could be A, B, or C depending on the stiffness of the segments.

 

[dik]

Pretend the member on the RHS is 'gone', since there is no restraint. Does that make the problem any easier?

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[KootK]

This is fun... and difficult.

I believe that point [A] moves upwards and does so regardless of the relative stiffness of the three members.

1) Taking moments about the central support reveals that there can be no horizontal reaction at the lower left support.

2) If there is no horizontal reaction and no moment at the lower left support, then the left member is completely straight and has no curvature along its length. I can prove this part separately if necessary.

3) If the left member has no curvature along its length then there is no rotation at point [A].

4) If the left member has no curvature along its length then there is also no moment at point [A].

Taking the above into account and simplifying the structure a bit, you wind up with a beam with a bizarre set of concurrent, pseudo boundary conditions at [A}

a) [A] does not rotate.

b) [A] experiences no bending moment.

I believe that the only admissible solution given these constraints is for the deformation pattern shown below to develop.

 

[BridgeSmith]

The answer is "d" - Point A will move up and to the right.

The rotation and bending of the top horizontal will move point A to the right. It may be a small fraction of the upward movement, but it's not zero.

I also have to disagree with Kootk. With the left side pinned there is a vertical reaction there, making the net vertical force at A less than the force on the right hand corner. There is a moment at A, and therefore also a horizontal reaction at the bottom left-hand support.

 

[KootK]

The left support is a vertical slider BridgeSmith. No vertical reaction there by definition.