Stress Around Bolt Hole Comparison Between A -...

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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

MSC Software Confidential

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


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


Determination of Stress Concentration Factor:

Pin stress concentration factor is determined from the following chart:

Hand Calculation Method (cont.)

4


Determination of Stress Concentration Factor: (cont.)

Using “Peterson’s stress concentration factors” charts


5


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


6


Calculations:


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:


Calculations: (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


Calculations: (cont.)


tbtbptptt

Total tensile stress:

Von-Mises stress:

Margin of Safety:

1

VM

ySF

YieldMS

tttttttttttttttttt

VM

2222

22

22222222


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


A Study Case (cont.)

Clamping Zone

(~ Bolt Head or

Washer Diameter)

Bolt Hole Location

One-Element-Away

Location

RBE2 (6 dofs) & CBUSH


Stress-at-bolt-hole


Max. Stress = 21.2 ksi


One-element-away stress


Max. Stress = 19.5 ksi


Out-Of-Clamping Zone stress


Max. Stress = 7.97

ksi


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


Tensile area:

2

1 1072.0188.019.019.04)( inTdWA holet


Hand Calculations Results (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:


Hand Calculations Results (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


Comparison Summary


• 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


Summary of Other Study Cases



At bolt hole location, stress is local and unrealistic ===> Margin

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 for

margin of safety calculation

Conclusions

Stress Around Bolt Hole Comparison Between A -...

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