1. University of Waterloo
Department of Mechanical Engineering
ME Mechanical Design 1
Partial notes – Part 6 (Welded Joints)
(G. Glinka)
Fall 2005

2. 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

3. Strength-Fatigue Analysis Procedure
Component
Geometry
Loading
Stress-Strain
Analysis
Strength
Allowable Load / Fatigue Life
Material
Properties
Information path in strength and fatigue life prediction procedures

4. A Welded Structure – Example
a) Structure
b) Component
c) Section with welded joint A sn
d) Weld detail A
Weld A σ

5. Load configuration and the global bending moment distribution along segments of telescopic crane boom

6. 1 2 b) F
Segment No. 2 c)
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

7. Typical geometrical weld configurations
g = h
l = hp
Butt welded joint
=tp hp t
T-joint with fillet welds
(V.A. Ryakhin et.al., ref. 29)

8. Stress concentration & stress distributions in weldments
Various stress distributions in a butt weldment; r A B C D E P M F
peak
hs n t
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).

9. Stress concentration & stress distributions in weldments
Various stress distributions in a T-butt weldment with transverse fillet welds; r t t1 E D B C A
peak n
hs F P M 
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).

10. Stress components in the weld throat cross section of butt weldment  L t
 = P/A
 = R/A
Resultant equivalent stress
A = t·L

11. (source: J.G. Hicks, ref. 41)

12. (source: J.G. Hicks, ref. 41)

13. 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
Stress path

14. 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)

15. T- butt weldment with non- load-carrying transverse fillet welds (static strength analysis not required!) R V P L t

16. (correct solid mechanics combination of stresses in the weld throat!!)
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!!) 1  2 R P L t n
 = Pcosα/A
1 = Pcosα/A
2 = R/A
A = t·cosα α
Resultant equivalent stress

17. 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 !!
1=P/A
2=R/a
Calculation of the transverse shear stress
1= X=P/A 1 x 2 R P L t n α

18. Stress components in the weld throat cross section plane in a T- butt weldment with load-carrying transverse fillet welds (the customary American method !!) 1 2 R P L t n
Resultant shear stress α
 = 0 !!
1= X=P/A
2=R/a 

19. EXAMPLE: Transverse fillet weld under axial loadingτ1 x
P/2 t 
EXAMPLE: Transverse fillet weld under axial loading

20. Fillet welds under primary shear and bending loadV α a)
τ1,M = σM M σM c)
Fillet welds under primary shear and bending load σV b) d)

21. 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 σM V σ
τ1= σ
Acceptable design:

22. 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 b
Weld
line b) c) r 2c d a) t h P

25. Unit moments of area of typical weld groups
Weld configurations
t - weld throat thickness
Iu - unit axial area moment of inertia, [m3]
Ju - unit polar area moment of inertia, [m3]
Unit moments of area of typical weld groups
From: B.J. Hamrock, ref.(26)
Note!
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):
for t =1

26. Stresses in welds under torsion and direct shear loads only
P = T
Shear stresses induced by the the direct force P
Shear stresses induced by the the torque T
Resultant shear stress
2P
1P x y
1T
2T
Stresses in welds under torsion and direct shear loads only

27. Combination of stress components induced by multiple loading modesz x y a) r Aw Ap V
(x,y) CG b)
(x,y) c)
Combination of stress components induced by multiple loading modes

28. 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:
The weld is acceptable if :
Where: ys is the shear yield strength of the: weld metal for fillet welds and parent metal for butt welds