stress around bolt hole comparison between a...
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MSC Software Confidential MSC Software Confidential
Stress Around Bolt Hole Comparison Between A Closed
Form Calculation Method and Finite Element Analysis
Results
2013 Regional User Conference
Presented By: Tuan Nguyen, Ph.D., P.E.
May 14, 2013
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In a FE model, a bolted joint can be modeled either by following
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/can’t be used for random analysis or any method
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 holt
is calculated using in-plane pin load, by-pass tension load, and
by-pass bending load as shown in the picture below
Stress concentration factors are also included in the calculation
Hand Calculation Method
3
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Determination of Stress Concentration Factor:
Pin stress concentration factor is determined from the following chart:
Hand Calculation Method (cont.)
4
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Determination of Stress Concentration Factor: (cont.)
Using “Peterson’s stress concentration factors” charts
Hand Calculation Method (cont.)
5
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Loads Determination: “Pin” and “By-pass” loads are determined
as following:
In-plane pin load: extracted loads from CBUSH that represents the bolt
By-pass tension and bending moment loads : extracted load within W =
4dhole from FE model using “Free Body/Interface” function in MSC Patran
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 factor W = 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.)
3
112
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
tttttttttttttttttt
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 bolt
hole to represent bolted joint clamping zone under bolt head or
washer
Maximum stress results from FE analysis will be derived at the
following 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 or
Washer Diameter)
Bolt Hole Location
One-Element-Away
Location
RBE2 (6 dofs) & CBUSH
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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:
2
1 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
FK
t
tbp
bypassttbp 7611072.0
5.3343.2)(
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) 4.00
By-pass Tension Stress Concentration Factor Kt(by-pass) 2.43
Out-of-plane Bending Stress Concentration Factor Kt(bend) 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