# Calculating total stress in bolts that holds an actuator?

1. Feb 23, 2012

### WillemBouwer

Hi All! I am currently busy working on a new knife gate valve design. I have an actuator with a mass of 200 kg attached at the top of the valve. The bottom plate of the actuator is 28 mm thick and I am going to use this plate directly to fasten the actuator(see attached drawing for plate dimensions).
The fastning bolts will be as specified:
2xM16 Bolts at ∅445 P.C.D and 4xM16 Bolts at ∅160PCD...
Bolt material is Stainless Steel 304 A2-70 with properties: (Note:Please advice if this is correct)
Ultimate Tensile Strength (Stu): 700 MPa
Tensile Yield Strength (Sty): 420 MPa
Ultimate Shear Strength (Ssu): 490 MPa

I would like to determine if the bolts will be sufficient to hold the actuator when the valve is fitted in a horizontal position?

Relevant equations:
Shear Stress:
For circular sections: Ss = (4/3)*(V/A)
Where V = applied force (N) and A = Cross-sectional area of the Bolts (mm^2)
Normal Yield Stresses:
FSy*(M*c/I)/Sty ≤ 100 %.
Where M is moment created by the Centre of Mass of the Actuator working at 300 mm from plate (N.m), c = radius of bolts core (mm) and I = Moment of inertia (mm^4)
σ= F/A
where F = Preload force inside bolt caused by specific torque applied to bolts (N)

My calcs:
Recommended Bolt torque is 160 N.m
T = 0.2DF ( This is an equations I know works for bolts)
Thus F = 160/(0.2*0.016) = 50 kN
and σ= F/A
gives σ = 50000/(∏*13.5^2)/4 = 349 MPa

Shear stress because of weight:
Ss = (4/3)*(V/A)
with V = 1962/6 = 327 N/bolt
Ss = (4/3)*(327/(∏*13.5^2)/4)
Ss = 3.02 MPa

Now here comes the problem: I am relitavely sure that the C.O.M of the actuator(situated 300mm from the bolts) causes a moment at the bolts, which causes normal bending stress?

Then σ = (M)*(c)/I
then σ = (327*300)*(6.75)/(∏*(13.5)^4/64)
= 406 MPa

But if this is the case the bolts will surely not hold the actuator, but I am confinced that it should!!!! Any verification on this will be much appreciated.

Next thing I should do will be to determine the max von mises stress and compare that to the proof stress of the bolt! Help on this is also needed...

Please check attached drawings for some info! Any replies is welcome!

Thanks

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2. Feb 23, 2012

### Mech_Engineer

Keep in mind that for a bolted joint you are designing its preload such that it is higher by some safety factor than the combination of forces on the joint's bolt pattern. As long as the bolts in the joint have preload in the joint, and there is no shear sliding in the joint, any single one of the bolts cannot have a moment on it (other than torsion caused by tightening). Instead, the applied moment is spread accross the bolt pattern as compressive and tensile forces (or shear as the case may be).

3. Feb 23, 2012

### nvn

WillemBouwer: As mentioned by Mech_Engineer, your bending stress calculation currently appears to be incorrect. Is the vertical axis of your coordinate system (CS) the z axis, or the y axis? Assuming your vertically upward CS axis is called y, then the bolt pattern moment of inertia is, Ix = summation[(y^2)*Ab]. Therefore, Ix = (4 bolts){[(0.5*165)*sin(45 deg)]^2}*(0.25*pi*13.5^2) = 4(58.3363^2)*Ab = 1 948 477 mm^4.

Therefore, bolt applied tensile stress due to applied moment currently appears to be, sigma = M*c/Ix = [(300 mm)(1962 N)](58.3363 mm)/(1 948 477 mm^4) = 17.62 MPa, not 406 MPa.

Last edited: Feb 23, 2012
4. Feb 24, 2012

### WillemBouwer

Thanks for the reply guys! I had a feeling the bending stresses was incorrect but knew the c.o.m should have some influence on the compression/tensile stress acting in the bolts!

nvn: The valve can be oriented in either the y or z axis as the vertical axis, so I have to bear in mind both. but if z is the vertical axis I don't think the bolts will fail at all, seeing that they only do I holding job!
I did not once think of this equation as I took a each bolt individually, but it makes sense to do them all together as they act together!

If I now have that Ss = 3.02 MPa, σ_preload stress = 359 MPa and σ_bending = 17.62 MPa then the von mises stress should be:
Svm = sqrt(S1^2 + S2^2 + S3^2 +3(Ss)^2)
= sqrt(359^2 + 17.62^2 - (359*17.62) + 3*(3.02)^2)
= 350 MPa
Is this correct or does it change for each bolt seeing that the bending stress is compressing for some bolts and works as tensile for others?

Then Nfs = 420/350 = 1.2 ? is this right?

5. Feb 26, 2012

### nvn

WillemBouwer: Your von Mises stress looks incorrect. Nonetheless, your shear stress is currently low; therefore, you currently do not need to worry about von Mises stress. I.e., you can currently neglect shear stress. You can currently assume approximately 30 % of the applied tensile stress goes to the bolt. And let's currently assume the torque uncertainty factor is 1.30; and let's assume the yield factor of safety is currently 1.30. I will continue using your bolt diameter in post 1, which is conservative. For A2-70 bolts, I think Sty = 450 MPa, not 420 MPa. Using these assumptions, the final, factored bolt axial stress is currently as follows.

sigma_f = 1.30*sigma_i + 0.30*1.30*sigma
= 1.30*349 + 0.30*1.30*17.62 = 460.6 MPa

Nfs = 450/460.6 = 0.9770

Therefore, this indicates you would need to decrease bolt installation torque to, e.g., 150 N*m.

Last edited: Feb 26, 2012
6. Feb 27, 2012

### WillemBouwer

Thanks nvn! I took the torque as 150 N.m and found that sigma_f = 431 MPa this gives a net safety factor of 1.04!!! This is okay I guess, seeing that we already worked at a safety factor of 1.3 for yielding!
So I will just state on my assembly bill that the recommended torque on the bolts should be 150 N.m...
Thanks for the help!!! Should be able to get the other valve sizes correct!!!