Post on 07-Apr-2015
Welded Joints in BendingWelded Joints in BendingWelded Joints in BendingWelded Joints in Bending
Overview
• Stressing of welded joints:– Bending analysis of welds– Stress Concentration– Fatigue of welded joints
Bending Analysis of Welds
• Bending analysis of welded structures follows on closely from analysis of torsional loading:– breaking the applied loads down into direct
(primary) loads (tension and/or shear loads) and (secondary) bending moment
– analysing the primary stresses due to the direct loads as force/area
– analysing the secondary stresses due to the bending moment, unit second moment of area Iu
Stressing of welds in combined bending/shearing
• For a cantilever with fillet welds along its top and bottom faces:
F
l
Stressing of welds in combined bending/shearing
• Replace applied load F with V and M:
V M
Stressing of welds in combined bending/shearing
• Vertical reaction is taken by primary shear stress:
• where A is the total throat area, in this case:
A
F
A
V'
hlhlA 414.1707.02
Stressing of welds in combined bending/shearing
• The moment M produces bending stresses in the welds
• It is usual to assume that this stress acts normal to the throat area
• True depth of the weld is usually small compared to other dimensions
• By treating the welds as lines we can use the unit second moment of area for bending
Stressing of welds in combined bending/shearing
• In this case:
d
b0.707h
2
2d
y
bx
2
2bdIu
hbA 414.1
Stressing of welds in combined bending/shearing
• Unit 2nd moment of area about horizontal axis is:
• Second moment of area is:
• Normal stress (at a distance y from the neutral axis) is:
2
2bdIu
I
Ty
uhII 707.0
Stressing of welds in combined bending/shearing
If there is no shear loading:• Assume that the maximum shear
stress in the weld is equal to the nominal tensile (or compressive) stress we have calculated based on the throat area
• Assess the strength of the weld by comparing this nominal shear stress with the allowable shear stress in the material.
Combining the shear and bending stresses
• Shigley et al use vectorial combination of stresses
• A better approach is to use Mohr’s circle (for 2 or 3 dimensional stresses)
+
2
Example
• Estimate the safety factor in the bracket if the maximum allowable stress is 120 MPa
120
120
F = 7.5 kN
6
6
6
60
Example
• Use the relationships from row 5 of the table in appendix A
60
dbhA 2707.0
db
dy
bx
2
22
223
223
2ydbyd
dIu
120
Example: Primary Stress• The primary stress is F/A (as always!)
23
3
m10273.1
12.0206.0106707.0
2707.0
dbhA
120
120
F = 7.5 kN
MPa89.510273.1
105.7'
3
3
A
V
Example: Secondary Stress
• The vertical centroid distance is:
• The unit second moment of area is:
mm48)12.0(206.0
12.0
2
22
db
dy
36
23323
223
m108.460
1048))12.0(206.0(1048)12.0(23
)12.0(2
223
2
ydbydd
Iu
Example: Secondary Stress
• The maximal secondary stress occurs furthest from the neutral axis (maximum y, AKA c = 72 mm)
MPa16.33
10954.1
1072105.76
33
XXI
My
46
63
m10954.1
108.460106707.0707.0
uhII
12072
Example: total stress• Combine the primary and secondary
stresses using Mohr’s circle:
+
2 = 19.6°
(33.16, 5.89)
(0, 5.89)
34.175 MPa
Example: Secondary Stress
• The maximal stress is 34.175 MPa, 9.8° off the horizontal and acting on the toe of the vertical weld
• This represents a safety factor (under static loading of a ductile material) of
5.3175.34
120n
Stress Concentrations
• For elastic materials nominal stress is
• Saint-Venant’s Principle says this is so beyond a characteristic length (b) from a stress raiser
F
F
bt
Fnom
t
b
Stress Concentrations• Maximum stresses
may be much larger than the nominal
• Stress concentration factor is:
F
nom
max
K
t
b
F
Stress Concentration
• Stress concentration factors are found empirically (look for them in tables)
• Stress concentrations are geometry and surface finish dependent.
stress concentration in a flat bar ofreducing section – note the blend radii
Stress Concentration• In ductile materials
stress concentrations are usually ignored due to material flow
• Stress concentrations must be accounted for in designs involving:– brittle materials (which
are very sensitive)– Fatigue loading– Impact loading
Photoelastic and FEA determination of stress concentrations in the flat bar of reducing section
Stress concentrations in welds
• Stress concentration is 1.2 on a reinforced butt weld
• Reduces to 1 if weld is “dressed”
Stress concentrations in welds
• Stress concentration at the end of a parallel fillet weld is 2.7
Stress concentrations in welds
• Fatigue Stress concentration factors (Kfs) for weld and parent metal:
• Reinforced butt weld 1.2• Toe of transverse fillet 1.5• End of parallel fillet 2.7• T weld with sharp corners 2.0
Fatigue Loading• Many materials
exhibit a fatigue limit; below this limit fatigue failure is unlikely.
• For steel the fatigue limit is around 50% of the UTS for static loading
• For aluminium it’s poorly defined but around 25% of UTS
Fatigue limit is shown on the S-N (endurance) diagram
Fa
ilure
str
ess
Number of cycles to failure
Fatigue limit
Welding & Fatigue Resources
• http://www.roymech.co.uk/Useful_Tables/Fatigue/Stress_concentration.html– Tables of stress concentration factors + design guide
• http://www.gowelding.com/– all manner of information
• Shigley, J.E., Mischke, C.R., Budynas, R.G. 2004. Mechanical Engineering Design (7th international edition), McGraw Hill.
• Gere, J.M. and Timoshenko, S.P., 1997. Mechanics of Materials (4th edition), PWS Publishing, Boston.