SME
Steel Design · Problem type
Fillet welds
Use this for “A plate is welded to a gusset by two ⅜ in E70 fillet welds, each 8 in long. Find the strength per inch and φRₙ.”
Diagram
The throat, the weld’s thinnest part, is 0.707w = 0.707 × 0.25 = 0.177 in.
Per inch: φRₙ = 0.75 × 0.6FEXX × 0.707w = 0.75 × 0.6 × 70 × 0.177 = 5.57 kip/in.
Both welds: 5.57 × 10 × 2 = 111 kips.
The section is enlarged; the plan is to scale along the welds.
This is an example. Type your own values to start a new problem.
tₑ (in)
=
0.707
×
w (in)
φrₙ (kip/in)
=
0.75
×
0.6
×
FEXX (ksi)
×
tₑ (in)
φRₙ (kip)
=
nw
×
L (in)
×
φrₙ (kip/in)
Formulas
tₑ
=
0.707
×
w
0.1768 = 0.707 × 0.25
φrₙ = 0.75 × 0.6 × FEXX × tₑ
5.5676 = 0.75 × 0.6 × 70 × 0.1768
φRₙ
=
nw
×
L
×
φrₙ
111.3525 = 2 × 10 × 5.5676
Assumptions
•
AISC 360-22, LRFD: φ = 0.75 on the stress 0.6FEXX acting over the effective throat.
•
Equal-leg fillets loaded along their length; the throat is the leg times sin 45°, or 0.707w.
•
nw welds of equal length L: one or two along the plate’s edges, a third across its end.
•
The base metal beside the welds is checked separately.
Step-by-step
WE KNOW
w = 0.25 in, FEXX = 70 ksi, L = 10 in, nw = 2
FIND
effective throat (tₑ), strength per inch of weld (φrₙ), strength of the welds (φRₙ)
Step 1 · Find effective throat (tₑ)
Use tₑ = 0.707 × w
The
throat
is
the
shortest
path
through
the
weld,
across
the
45°
face:
w
×
sin
45°.
tₑ = 0.707 × 0.25
tₑ = 0.17675 in
Step 2 · Find strength per inch of weld (φrₙ)
Use φrₙ = 0.75 × 0.6 × FEXX × tₑ
Each inch of weld shears across its throat at 0.6FEXX; φ = 0.75.
φrₙ = 0.75 × 0.6 × 70 × 0.17675
φrₙ = 0.45 × 70 × 0.1768
φrₙ = 31.5 × 0.1768
φrₙ = 5.567625 kip/in
Step 3 · Find strength of the welds (φRₙ)
Use φRₙ = nw × L × φrₙ
nw
welds,
each
L
inches
long,
each
inch
carrying
φrₙ.
φRₙ = 2 × 10 × 5.567625
φRₙ = 20 × 5.5676
φRₙ = 111.3525 kip
Check
Put the numbers back in. Both sides should match.
0.17675 = 0.707 × 0.25 ✓
5.567625 = 0.75 × 0.6 × 70 × 0.17675 ✓
111.3525 = 2 × 10 × 5.567625 ✓
Topic check
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