Page 106 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch03.qxd 9/29/05 5:05 PM Page 3.38

CONNECTIONS

3.38 CHAPTER THREE

where A wi = effective area of weld throat of any ith weld element, in 2
F wi = 0.6F EXX (1 + 0.50 sin 1.5 θ)f(p) (3.16)
f(p) = [p(1.9 − 09p)] 0.3 (3.17)
F wi = nominal stress in any ith weld element, ksi
F wix = x component of stress F wi
F wiy = y component of stress F wi
p =∆ i /∆ m , ratio of element i deformation to its deformation at maximum stress
∆ m = 0.209(θ+ 2) −0.32 w, deformation of weld element at maximum stress, in (mm)
∆ i = deformation of weld elements at intermediate stress levels, linearly proportioned
to the critical deformation based on distance from the instantaneous center of
rotation r i , in
r∆
= i u
r crit
∆ u = 1.087(θ+ 6) −0.65 w ≤ 0.17w, deformation of weld element at ultimate stress (fracture),
usually in element farthest from instantaneous center of rotation, in
w = leg size of the fillet weld, in
r crit = distance from instantaneous center of rotation to weld element with minimum ∆ u /r i
ratio, in
The calculations can be made graphically using the load–deformation curves in Fig. 3.26.
For example, to find the strength of the concentrically loaded weld group shown in Fig. 3.25,
first the least ductile weld (greatest θ) is determined. In this case it is the transversely loaded
weld. By drawing a vertical line from the point of fracture, the strength increase or decrease for
the remaining elements can be determined. In this case the strength of the weld group is found
to be

φR w = (D)(1.392)[1.5(1) + 1.29(1.41) + 0.83(1)] = 578D

1
where D is the weld size in / 16ths and 1.392 is the design strength of a weld with E70 electrodes,
1
kip/in per / 16th. The latter is determined from
1
1
φR n =φF w A w = 0.75 × 0.60 × 70 × ( / 16) × 0.707 = 1.392 kips/in per / 16th
For fillet weld groups loaded concentrically, consisting of welds in the transverse and longitudi-
nal directions, then the combined nominal strength of the weld group is permitted to be taken as the
greater of the following:
(3.18)
R n = R wl + R wt
(3.19)
R n = 0.85R wl + 1.5R wt
where R wl = total nominal strength of longitudinally loaded fillet welds
R wt = total nominal strength of transversely loaded fillet welds

R wl and R wt are determined from basic provision for nominal strength,

(3.20)
R n = F w A w
2
where F w = 0.60 F EXX is the nominal strength of the weld metal, ksi, and A w , in , is the effective area
of the weld.

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