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8/9/2019 Stresses Around Bolt Hole
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MSC Software Confidential
In a FE model, a bolted joint can be modeled either by followi
approaches:
1. Solid elements/Contact elements/preload model
Pros: can closely simulate a bolted joint/reduce local stress issue
Cons: time-consume-modeling and running effort/not suitable for a
complex or large model/cant be used for random analysis or any me
using modal approach
2. Shell/solid elements with wagon wheel RBE2 and CBUSH elements
Pros: less-time-consume-modeling and running effort/suitable for
random analysis or any method using modal approach
Cons: local stress results around bolt hole due to rigid body RBE2
This paper is to present stress comparison around bolt hole
between FE analysis results (Approach #2) and a hand
calculation method
Introduction
2
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In the hand calculation method, maximum stress around bolt
is calculated using in-plane pin load, by-pass tension load, an
by-pass bending load as shown in the picture below
Stress concentration factors are also included in the calculat
Hand Calculation Method
3
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Determination of Stress Concentration Factor:
Pin stress concentration factor is determined from the following char
Hand Calculation Method (cont.)
4
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Determination of Stress Concentration Factor: (cont.)
Using Petersons stress concentration factors charts
Hand Calculation Method (cont.)
5
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Loads Determination: Pin and By-pass loads are determ
as following:
In-plane pin load: extracted loads from CBUSH that represents the b
By-pass tension and bending moment loads : extracted load within W
4dholefrom FE model using Free Body/Interface function in MSC Pa
Hand Calculation Method (cont.)
6
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Calculations:
Hand Calculation Method (cont.)
7
Tensile area:
1)( TdWA holet
t
tp
pinttpA
FK )(
1. Tensile stress from in-plane pin load:
Where
Ftp= In-plane pin load (lbs)
Ftbp= By-pass tension load (lbs)
Kt(pin)= In-plane pin load stress concentration factor
Kt(bypass)= By-pass tension load stress concentration factorW = assumed width = 4dhole
T1= flange thickness
t
tbp
bypassttbpA
FK )(
2. Tensile stress from by-pass tension load:
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Calculations: (cont.)
Hand Calculation Method (cont.)
3112
1TdWI hole
Moment of inertia:
2
1
)(3
1
1
)(
1
)(
6
12
1
22
TdW
MK
TdW
TM
KI
TM
Khole
bp
bendt
hole
bp
bendt
bp
bendttb
3. Bending Stress from by-pass bending moment:
Where
Mbp= By-pass bending moment (in-lbs)Kt(bend)= Bending stress concentration factor
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Calculations: (cont.)
Hand Calculation Method (cont.)
tbtbptptt Total tensile stress:
Von-Mises stress:
Margin of Safety:
1
VM
ySF
YieldMS
tt
tttttttttttttttt
VM
2222
22
22222222
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A mounting flange FE model with wagon wheel RBE2 and
CBUSH element at the bolt hole locations is created and
analyzed under a static inertial load
Several layers of concentric circles are created around each
hole to represent bolted joint clamping zone under bolt head
washer
Maximum stress results from FE analysis will be derived at tfollowing locations:
At bolt hole location
At one-element-away from bolt hole location
Right outside of the clamping zone
A Study Case
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A Study Case (cont.)
Clamping Zone
(~ Bolt Head oWasher Diame
Bolt Hole Location
One-Element-Away
Location
RBE2 (6 dofs)
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Stress-at-bolt-hole
A Study Case (cont.)
Max. Stress = 21.2 ksi
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One-element-away stress
A Study Case (cont.)
Max. Stress = 19.5 ksi
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Out-Of-Clamping Zone stress
A Study Case (cont.)
Max. Stress = 7.97ksi
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Hand Calculations Results Hole diameter dhole= 0.19
Width W = 4xdhole= 4x0.19 = 0.76 Plate thickness T1= 0.188
In-plane pin load Ftp= 95.6 lbs
By-pass tension load Ftbp= 33.5 lbs
By-pass bending moment Mbp= 7.5 in-lbs
Kt(pin) = 4.0
Kt(bypass) = 2.43 Kt(bend) = 1.77
A Study Case (cont.)
Tensile area:
21 1072.0188.019.019.04)( inTdWA holet
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Hand Calculations Results (cont.)
A Study Case (cont.)
psiA
FK
t
tp
pinttp 568,31072.0
6.950.4)(
1. Tensile stress from in-plane pin load:
psiA
F
Kt
tbp
bypassttbp 7611072.0
5.33
43.2)(
2. Tensile stress from by-pass tension load:
psi
TdW
MK
hole
bp
bendttb 918,3188.019.076.0
5.7677.1
622
1
)(
3. Bending Stress from by-pass bending moment:
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Hand Calculations Results (cont.)
A Study Case (cont.)
Total tensile stress:
VMtbtbptptt psi 247,8918,3761568,3
From FE results, stress at bolt hole is:
psiFE 200,21
Thus,
6.2247,8
200,21
tt
FE
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Comparison Summary
A Study Case (cont.)
Hand calculated stress is smaller than
stress at bolt hole location (< 2.6x) Hand calculated stress is smaller than
stress at one-element-away location
(< 2.4x)
Hand calculated stress is slightly
greater than stress at out-of-clamping
zone location (> 1.03x)
Study Case
dbolt (in) 0.190
dhole (in) 0.190
Sectional Cuts Dimensions dH (in) 0.760
Flange 1 Thickness T1 (in) 0.188
Emembers (psi) 1.00E+07
Member Yield Strength (psi) 35,000
Member Ultimate Strength (psi) 42,000
Safety Factor on Yield 1.15
Safety Factor on Ultimate 1.25
In-plane Pin Load (lbs) 95.6
By-Pass Tension Load (lbs) 33.5
By-Pass Bending Moment (in-lbs) 7.5
dhole/dH 0.2500
T1/dhole 0.9895
Pin Stress Concentration Factor Kt(pin) 4.00By- pass Te ns ion Stre ss Conce ntrati on Factor Kt(by- pass) 2. 43
O ut- of -p la ne Be nd in g S tres s Co nce nt rat io n F act or Kt (be nd ) 1.77
Moment of Inertia (in^4) 0.0003
Tensile Area (in^2) 0.1072
In-plane Pin Load Tension Stress (psi) 3,568
By-pass Tension Load Stress (psi) 761
By-pass Moment Bending Stress (psi) 3,918
Total Tensile Stress (psi) 8,247
Von-Mises Stress (psi) 8,247
Hand Calculation Von-Mises Stress (psi) 8,247
FE Results One-Element-Away Von-Mises Stress (psi) 19,500
(One-Element-Away FE Result / Hand Calc. Result) Ratio 2.4
FE Results at Bolt Hole Location Von-Mises Stress (psi) 21,200
(Bolt Hole FE Result / Hand Calc. Result) Ratio 2.6
FE Results at Out-of-Clamping Zone Location Von-Mises Stress
(psi) 7,970
(Bolt Hole FE Result / Hand Calc. Result) Ratio 0.97
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Summary of Other Study Cases
A Study Case (cont.)
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At bolt hole location, stress is local and unrealistic ===> Marg
of safety will be too conservative
At one-element-away location (that is still within bolt head or
washer clamping zone), stress is more reasonable to be used
margin of safety calculation
Conclusions