Permanent joints
List of topics:
• Welding
• (Brazing and soldering)
• Rivets
• Adhesive bonding
1
Butt welds
Juvinall and Marshek
Shigley, Fig. 9-7a
F
if in tension (as shown in figure)
hL
F
if in shear
hL
Stress concentration along line at A
Grind off reinforcement if fatigue loading
2
Fillet welds
Juvinall and Marshek
t
h
t t h 4t 2 h 2 h 2 t 0.707h
2
h
Shear stress analysis at 45o:
Conservative (safe ) approximation of stress state
1.414F F F F
hL A tL 0.707hL
3
Analysis process for combined
loading of welds
• Examine primary shear stresses due to external
forces
• Examine secondary shear stresses due to torsion
and bending moments
• Examine strength of parent metals
(in members)
• Estimate strength of deposited weld metal
(in filler)
• For static loads: DE criterion
• For fatigue loads: modified Goodman criterion
4
Stress from torsion
Shigley, Fig. 9-12
• Primary shear
V
' , A : throat area
A
• Secondary shear
Tr
''
J
J : polar moment of inertia about c.o.g G
r : distance from G to point of interest
(i.e. worst case)
5
Finding G and J
Welds can be modelled as lines and the polar
second moment of area is calculated as
J 0.707hJ u , J u : unit second polar moment of area
Shigley, Table 9.1 (partial)
6
Stress from bending
Shigley, Fig. 9-17
• Primary shear
V
' , A : throat area
A
• Secondary shear
Mc
''
I
b(d 2 0.707 h)3 bd 3
I
12 12
( x y )3 x3 3x 2 y 3xy 2 y 3
bd 2 bd 2
I 0.707 h Iu
2 2
7
Finding G and I
Welds can be modelled as lines and the second
moment of area is calculated as
I 0.707hI u , I u : unit second moment of area
hb
Shigley, Table 9.2 (partial)
8
Strength of welds, fatigue
Shigley, Table 9-3
Juvinall and Marshek
* 9
Bolt and rivet failure
a) Single lap joint axial loading (shear in
rivet)
Six different types of failure:
b) Bending M Ft / 2
Mc / I without stress concentration
either in rivet or member
c) Pure shear F / A, A r 2
10
Shigley, Fig. 8-23
Bolt and rivet failure
F F
A t ( w nd )
d) Rupture of one of the plates
n : # of rivets
d : diameter of rivets
e) Crushing of rivet F
, A td
Crushing of plates A
t : thickness of thinnest plate
d : diameter of rivet
Shigley, Fig. 8-23
11
Bolt and rivet failure
f) Edge shearing or tearing g)
Avoid by having rivets at least 1.5
diameter from edge
12
Shigley, Fig. 8-23
Adhesive bonding and design
considerations
Shigley, Fig. 9-24
• Low weight
• Prevents stress concentrations due to holes and
notches
• Can use thinner substrate materials
• Dissipates energy (noise and vibration reduction)
• Important to prepare surface (roughened and
cleaned)
• Have environmental limitations since temperature
and moisture affect materials
• Viscoelastic behaviour
• Glass transition temperature very important, avoid
brittleness
• Thin layer
Good in shear
Poor in peel and bending 13
Bonding mechanisms
• Secondary bonds between atoms in close
proximity
• Enhanced bond strength from abrasion and
grit blasting of substrate (rough surface!)
• Some products work better at creating
secondary bonds with substrate. Table
6.8.2b in Marks (next page)
• Strength and stiffness come from
deformation and viscoelastic properties
• Dependent on:
loading rate
temperature
moisture (avoid at all costs)
• Respect shelf life
• Service temperature > Tg + 50oC
for application of adhesive
14
Performance of adhesive resins
15
Types of joints
Shigley, Fig. 9-25
• Bending moment in (a) and (c)
• Shear is good!
• Peeling is bad! (c) better than (a)
• Large shear area desirable
• Best uniformity
16
Types of joints
Shigley, Fig. 9-25
Sources of stress concentration in adhesives
• Abrupt angles
• Changes in material properties
• Sharp corners (very detrimental to brittle
adhesives)
• Residual stresses from high temperature
curing of adhesive
• Expansion/contraction on rigid substrate 17
18
Shigley, Fig. 9-28
Joint efficiency
UTS of joint
e
UTS of substrate
e < 30%
e = 60%
e ~ 65%
e = 70%
e = 90%
e ?!
e ?!
e?
Shigley, Fig. 9-25
19
Bond design
Shigley, Fig. 9-29
20
Bond design
Shigley, Fig. 9-29
21
