TO FIND DEFLECTION

[varatharajan]

HELLO EVERYONE,

HEREBY I ENCLOSED THE PICTURE OF THE BLOCK. I WANT TO FIND THE DEFLECTION ON BLOCK AT 35mm FROM GROUND DUE TO 2x M12 SCREWS WITH TORQUE 120Nm.

I FOUND PRACTICAL DEFORMATION AS 0.011mm. BUT I COULD NOT GET THE THEORETICAL SOLUTION FOR THIS PROBLEM. PLEASE ANYONE HELP ME TO GET THEORETICAL DEFORMATION.

 

THANK YOU,

 

REGARDS

VARATHA

[Bender]

What are the screws screwed into? The drawing doesn't show any thread.

What do you mean by deflection at 35 mm from ground? In what direction?

How did you measure the deformation?

 

It is in general bad manners to write everything in capital letters.

[Curiatron]

In general, beam deflection is a function of the following, which we need to even begin to analyze your problem.

1. Loading - location and quantity
2. Beam cross section shape
3. Beam material (elastic property)

Also, the specific deflection equation used will depend on:

• Beam loading - is it a continuous load or point load? If point loaded, how many, and located where on beam?
• How is beam supported? e.g. cantilevered? simply supported at both ends?

 

A free body diagram would help us better understand your problem. 

See https://en.wikipedia.org/wiki/Deflection_(engineering) for more information on beam deflection.

[studiot]

I am guessing here because the OP is far from clear but

I think the OP is referring to tightening down a block onto an unyielding sole or ground plate with his setscrews and a torque wrench.

This will obviously cause an elastic shortening of the block, which he refers to as the 'deflection'.

There is no reason for the block to bend, unless other unspecified forces are also acting.

However, varatharajan, you have to give the dimensions of the block and specify its material to solve this question.

Since practical measurement was mentioned, it is necessary to torque those screws up in stages or ther will be some warping forces involved.

Edited July 25, 2017 by studiot

[Bender]

He might also be referring to the lateral thickening (poisson effect).

[varatharajan]

Thanks for all whoever replied me. The topic that i posted was mine first post. Sorry for the mistakes that I made, I would like to correct myself. Now I uploaded the detailed drawing of the problem. I made the practical measurement of the deformation using CMM(coordinate measuring machine).

I want to find the deformation where I specified, when I apply the torque of 120Nm on both the screws.

All dimensions are in millimeters. 

Edited July 25, 2017 by varatharajan

[Bender]

You first need to calculate the force you are applying with each bolt. Without checking the equations used, I get 50 kN for each bolt from this online calculator. According to my mechanical bible this is a bit bellow the max force for the bolts used, so it is plausible.

Now you divide this force over the area to get the stress. Combined with the Young modulus, you get the strain. Multiply with 35 mm, and you have your (approximate) result. Obviously, there will be pretty large errors introduced everywhere, especially in deriving the force, but the order of magnitude should be good.

[studiot]

If you prefer to use a formula to calculate the bolt force, the standard one is

 

T = c*d*F

Where

T is the required tightening torque
d is the bolt diameter
F is the initial bolt force

c is a constant, default value 0.2

 

Use of the default value leads to the 50 kN mentioned by Bender.

Using this, and deducting the bolt hole area from your stated area I make the calculated shortening 0.005 mm.

 

Good site linked BTW Bender. +1

[varatharajan]

Thank you for everyone who replied me. I made a calculation with force of 50kN and I hope that we need to consider the screw elongation in this case. I calculated for one force, but  I don´t know how to use for two force. If I multiply the answer with 2 I found very big difference with practical value. so please help me to get correct answer.

I enclosed the image of my calculation with this post.

Regards,

Varatha.  

[studiot]

1) There are two bolts so F = 2 * 50kN

2) Your section BB is shown looking up into the thicker part of the block including the overhang. You should be using the area not including the overhang.

3) The tension extension of the bolts and the compression shortening of the block are of the opposite sign. How this affects the measured distance between the sole plate and the overhang depends upon the method of measurement and the foundation conditions of the sole plate.

 

Edited July 26, 2017 by studiot

[Bender]

The bolt elongation is irrelevant.

Whether you use flexible bolts with very large deformation or stiff bolts with small deformation, that doesn't (significantly) change the force on the block.

[studiot]

12 hours ago, Bender said:

The bolt elongation is irrelevant.

Whether you use flexible bolts with very large deformation or stiff bolts with small deformation, that doesn't (significantly) change the force on the block.

Yes it is irrelevant to the force in the bolts, but not to the changes of length and strain and hence distance measurements. I assume that was why you (rightly) asked the question how were the distance measurements made. The OP states "I want to calculate the 'deflection' at this point on the surface".

But the deflection from what?

A surface plate the whole assembly is standing on?

The contact surface between the sole plate and the block?
 

I agree that between any two sections or marks on the unstressed block, the compression will only depend upon the applied force, not the method by which it is applied.
However something must change position in the system, so if measurement is made from an external reference, this must be taken into account.

 

A question for varatharajan.

It is possible to have stress without strain or strain without stress.

Can you say how?

Edited July 27, 2017 by studiot