Page 133 - Analysis and Design of Machine Elements

Figure 5.3 Loads on a butt welded joint. Permanent Connections 111

are first decomposed into typical loads, that is, tension or compression forces, torques
or moments, as shown in Figure 5.3. The loads on each weld under each type of load
are then analysed separately and combined vectorially to determine the maximum load.
The common potential failure mode under these loads is fracture.
Assume stresses are uniformly distributed at weld cross sections. The following
section introduces strength analysis of butt welds and fillet welds.
5.2.3.1 Butt Welds
For a single V-groove butt weld loaded by either tensile or compressive force F, the weld
strength is analysed against the average normal stress as
F
= ≤ [ ] (5.4)
lt
Similarly, the shear strength due to shear load F against the average shear stress is
s
F s
= ≤ [ ] (5.5)
lt
And the strength due to moment loading M or M is calculated by
y z
6M y
= 2 ≤ [ ] (5.6)
lt
or
6M z
= ≤ [ ] (5.7)
2
l t
5.2.3.2 Fillet Welds
When a fillet weld joint carries a transverse load, the weld seam along the horizon-
tal plane is subjected to shear stress, while along the vertical plane this is a tensile (or
compressive) stress, as illustrated in Figure 5.4. The size of a fillet weld is defined as leg
length k, and, although not necessary, the two legs are usually of the same length. When
calculating transverse shear stresses and axial stresses, throat length m is assumed to be
∘
in a 45 orientation from the intersection of the plates to the straight line connecting the
ends of the two legs. For the usual convex weld with equal legs, m = 0.707 k.Thethroat
area used for stress calculations is then the product of ml,where l is the length of weld.
Since fillet welds usually fail in the throat section, the throat stresses are thus usu-
ally used in design. The stress and strength at the throat section of a fillet weld can be
approximately calculated as
F F
∘ = ≤ [ ] (5.8)
sin 45 kl 0.707kl