Transcript Slide 1

University of Waterloo
Department of Mechanical Engineering
ME 322 - Mechanical Design 1
Partial notes – Part 6 (Welded Joints)
(G. Glinka)
Fall 2005
1. Introduction to the Static Strength Analysis
of Welded Joints
•
•
•
•
•
The structural nature of welded joints
Static strength of weldments
The customary American method (AWS)
Simple welded joint analysis
Example
Strength-Fatigue Analysis Procedure
Material
Properties
Component
Geometry
Loading
Stress-Strain
Analysis
Strength
Analysis
Allowable Load / Fatigue Life
Information path in strength and fatigue life prediction procedures
A Welded Structure – Example
a) Structure
b) Component
Weld A
H
Q
F
d) Weld detail A
c) Section with welded joint
Weld
sn
A
R
P
V
σ
σ
Load configuration and the global
bending moment distribution along
segments of telescopic crane boom
b)
Segment No. 2
2
1
F
c)
F
a) Load configuration in two-segment telescopic crane boom, b) welded
box cross section of the boom, c) out of plane web deflections of the boom
box cross section
Typical geometrical weld configurations
l = hp
g=h
Butt welded joint
=tp
hp
t
T-joint with fillet welds
(V.A. Ryakhin et.al., ref. 29)
Stress concentration & stress distributions in
weldments
peak
E
n
r
hs
D
P
B
n
peak
F
t
C
A
M
C
Various stress distributions in a butt weldment;
• Normal stress distribution in the weld throat plane (A),
• Through the thickness normal stress distribution in the weld toe plane (B),
• Through the thickness normal stress distribution away from the weld (C),
• Normal stress distribution along the surface of the plate (D),
• Normal stress distribution along the surface of the weld (E),
• Linearized normal stress distribution in the weld toe plane (F).
© 2004 Grzegorz Glinka. All rights reserved.
Page 8
Stress concentration & stress distributions in
weldments
t1
peak
E
r
hs
D


n
M
A
t
B
C
P
F
C
Various stress distributions in a T-butt weldment with transverse fillet welds;
• Normal stress distribution in the weld throat plane (A),
• Through the thickness normal stress distribution in the weld toe plane (B),
• Through the thickness normal stress distribution away from the weld (C),
• Normal stress distribution along the surface of the plate (D),
• Normal stress distribution along the surface of the weld (E),
• Linearized normal stress distribution in the weld toe plane (F).
Stress components in the weld throat cross
section of butt weldment
 = P/A
 = R/A
Resultant equivalent stress
A = t·L
 eq   2  3  2 
2
R
P
L


P
R
t
(source: J.G. Hicks, ref. 41)
(source: J.G. Hicks, ref. 41)
Static strength analysis of weldments
•The static strength analysis of weldments requires the determination of stresses in
the load carrying welds.
•The throat weld cross section is considered to be the critical section and average
normal and shear stresses are used for the assessment of the strength under axial,
bending and torsion modes of loading. The normal and shear stresses induced by
axial forces and bending moments are averaged over the entire throat cross section
carrying the load.
•The maximum shear stress generated in the weld throat cross section by a torque
is averaged at specific locations only over the throat thickness but not over the
entire weld throat cross section area.
Non-load
carrying welds
Load carrying
welds
Definition of the weld throat thickness for
various geometrical weld configurations
Welds with
equal legs
Welds with
unequal legs
(source: J.G. Hicks, ref. 41)
T- butt weldment with non- load-carrying transverse
fillet welds (static strength analysis not required!)
V
R
P
L
P
R
t
V
Stress components in the weld throat cross section plane in a
T- butt weldment with load-carrying transverse fillet welds
(correct solid mechanics combination of stresses in the weld throat!!)
 = Pcosα/A
1 = Pcosα/A
2 = R/A
Resultant equivalent stress
2
2
 eq   2  3   1    2  
R

P
A = t·cosα

1
2

L
α
t
n
R
P
Stress components in the weld throat cross section plane in a
T- butt weldment with load-carrying transverse fillet welds
(simplified combination of stresses in the weld throat cross section according
to the customary American method !!)
 = 0 !!
Calculation of the transverse shear stress
1=P/A
1= X=P/A
2=R/a

R
P
 1    2 
2
 eq  3 2
1
x
2
L
α
t
n
R
P
2
Stress components in the weld throat cross section plane in a
T- butt weldment with load-carrying transverse fillet welds
(the customary American method !!)
Resultant shear stress
 = 0 !!
1= X=P/A
2=R/a

R
P
 1    2 
2
 eq  3  
1

2
L
α
t
n
R
P
2
EXAMPLE: Transverse fillet weld under axial loading
1   x 
P
2lt
P
2lh cos 
P

2lh cos 45
P

1.414lh

t
x
P/2
x
 eq  3 1 
τ1
3P
P
 1.225
1.414lh
lh
© 2004 Grzegorz Glinka. All rights reserved.
Page 19

P/2
Fillet welds under primary shear and bending load
a)
V
b)
σV
V  V
t b
 1,V  V
b
α
V
d
d
h
t
d)
l
c)
σV
V l 
2  V l
 M  M c 
I
t bd 2 t bd
σM
 1,M   M
τ1,M = σM
M
σV
V
σM
σM
σM
σV
2
Fillet welds in primary shear and bending:
the American customary method of combining the primary shear and bending shear stresses
(according to R.C.Juvinal & K.M. Marshek in Fundamentals of Machine Component Design, Wiley, 2000) )
σV
σ
τ1= σ
 1     V2   M2   1,2V  1,2 M
V
2
2



2
 1  V    V  l   V 1  l 2
d
t b   t bd  t b




σM
d)
Acceptable design:
 1  3ys
σM
σ
or
σV
V 1  l 2   ys
d2
3
t b
τ1= σ
© 2004 Grzegorz Glinka. All rights reserved.
Page 21
Idealization of welds in a T- butt welded joint; a) geometry and
loadings, b) and c) position of weld lines in the model for
calculating stresses under axial, torsion and bending loads
Mb
Tr
Tr
b)
P
a)
Mb
P
b
d
b
h
t
c)
2c
P
P 
;
2td
r
Mb  c
b 
Iw
2c
r
r
d
b
2c
T
r
Tr  r

;
Jw
Weld
line
d
b
c  or
2
2
2c
Weld
line
It is customary assumed that stresses in the weld throat cross section induced by bending
and torsion loads can be treated as lines of thickness ‘t’ and length ‘d’. The bending normal
stresses are subsequently calculated using the simple bending formula.
b 
Mb c
Iw
The moment of inertia Ix and Iy are calculated for the entire group of welds carrying the
bending moment, assuming that they are lines of thickness ‘t’. In the case of the two welds
shown in the Figure above the moments of inertia are:
Iw, y
d  t 3 t  d  b2
t d3


and I w , x 
6
2
6
Parameter ‘c’ is the distance from the neutral axis to the point on the weld line furthest from
the neutral axis of the group of welds being analyzed. In the case of the two welds shown in
the Figure it is:
c
b
d
or c 
2
2
The shear stress induced by a torque is calculated using the simple shear stress formula:
T
r
Tr r

Jw
The polar moment of inertia, Jw, is calculated for the entire group of welds carrying the
torque, assuming that they are lines as defined above. In the case of the two welds shown
in the Figure the polar moment of inertia is:

2
2
d  t 3 td 3b  d
Jw 

6
6

Parameter ‘r’ is the distance from the center of gravity of the group of welds being analyzed
to the furthest point on the weld line. In the case of the two welds shown in the Figure it is
the distance from the gravity center of the group of welds to the end of the weld:
2
d  b
r     
 2  2
2
Unit moments of area of typical weld groups
Weld configurations
t - weld throat thickness
Iu 
d3
12
Iu - unit axial area moment
of inertia, [m3]
Ju - unit polar area moment
of inertia, [m3]
Note!
Iu 
d3
6
The handbook ready made formulas for
the unit area moments of inertia are
approximate! The terms (bt3) or (dt3) are
sometimes omitted when the parallel axis
theorem is used!
It should be for example (the bottom
case):
I
bd2
Iu 
2
b t3 b t  d2

6
2
b bd2 bd2
Iu  

6
2
2
From: B.J. Hamrock, ref.(26)
I  t  I u  0.707h  I u ;
for t =1
J  t  J u  0.707h  J u ;
y
2T
Stresses in welds under torsion
and direct shear loads only
1T
y
1P
Shear stresses induced by
the the torque T
Shear stresses induced by
the the direct force P
1T
x
2T
2P
Resultant shear stress
T
P=


 1T   1P 
2
  2T   2 P 
2
Combination of stress components induced by multiple loading modes
a)
Aw
b)
c)
y
r
y
r
(x,y)
y
z
x
(x,y)
CG
Tr
P 
x
P
V
Ap
M
z
P
Aw
Tr rmax
 Tr 
J w,CG
   T   V   P   M    yield 
r
M 
M cy
V 
VQ
Ixt
 ys
3
I w, x
Static Strength Assessment of Fillet Welds
The American customary method: It is assumed that the weld throat is in shear for all
types of load and the shear stress in the weld throat is equal to the normal stress
induced by bending moment and/or the normal force and to the shear stress induced by
the shear force and/or the torque. There can be only two shear stress components
acting in the throat plane - namely 1 and 2 . Therefore the resultant shear stress can
be determined as:
   
2
1
2
2
The weld is acceptable if :
   ys 
 ys
3
Where: ys is the shear yield strength of the: weld metal for fillet welds and parent
metal for butt welds