SME
Steel Design
LRFD
Use this for “A beam carries dead load 20 kips, live load 30 kips and snow 10 kips. Which LRFD combination governs, and what is U?”
Chart
Ringed: Factored load, U = 77 kip
Dead load D = 20 kip
Live load L = 30 kip
Snow load S = 10 kip
Factored load U = 77 kip
Governing G = 1.2D + 1.6L + 0.5S
This is an example. Type your own values to start a new problem.
U₁ (kip)
=
1.4
×
D (kip)
U₂ (kip)
=
1.2
×
D (kip)
+
1.6
×
L (kip)
+
0.5
×
S (kip)
U₃ (kip)
=
1.2
×
D (kip)
+
1.6
×
S (kip)
+
L (kip)
D, L and S are the dead, live and snow loads; U₁, U₂ and U₃ are the three factored combinations.
U
Factored load
worked out (not typed) · kip
G
Governing
worked out (not typed)
Formulas
U₁
=
1.4
×
D
28 = 1.4 × 20
U₂
=
1.2
×
D
+
1.6
×
L
+
0.5
×
S
77 = 1.2 × 20 + 1.6 × 30 + 0.5 × 10
U₃
=
1.2
×
D
+
1.6
×
S
+
L
70 = 1.2 × 20 + 1.6 × 10 + 30
U
=
max(
U₁
,
U₂
,
U₃
)
77 = max(28, 77, 70)
G
=
the
combination
with
the
largest
of
U₁
,
U₂
and
U₃
77
≥
70,
77
≥
28,
so
1.2
D
+
1.6
L
+
0.5
S
Assumptions
•
ASCE 7-22 strength combinations with no wind or seismic; roof live load is not combined with snow.
•
Combination 3 takes L in full; ASCE 7 allows 0.5L where L₀ ≤ 100 psf, except garages and assembly.
•
D, L and S are service (unfactored) loads on the same member.
•
The largest combination U governs: the member needs design strength φRₙ ≥ U.
Step-by-step
WE KNOW
D = 20 kip, L = 30 kip, S = 10 kip
FIND
combination 1 (1.4D) (U₁), combination 2 (U₂), combination 3 (U₃), factored load (U), governing (G)
Step 1 · Find combination 1 (1.4D): U₁
Use U₁ = 1.4 × D
Dead load alone, raised by 1.4: it governs when the dead load dwarfs the others.
U₁
=
1.4
×
20
U₁
=
28
kip
Step 2 · Find combination 2 (U₂)
Use U₂ = 1.2 × D + 1.6 × L + 0.5 × S
Live load at its full factor 1.6, with snow along at its companion factor 0.5.
U₂
=
1.2
×
20
+
1.6
×
30
+
0.5
×
10
U₂
=
24
+
48
+
5
U₂
=
77
kip
Step 3 · Find combination 3 (U₃)
Use U₃ = 1.2 × D + 1.6 × S + L
Snow at its full factor 1.6, with the live load along unfactored (factor 1).
U₃
=
1.2
×
20
+
1.6
×
10
+
30
U₃
=
24
+
16
+
30
U₃
=
70
kip
Step 4 · Find factored load (U)
Use U = max(U₁, U₂, U₃)
The member must survive the worst case, so the largest combination is the design load.
U
=
max(28,
77,
70)
U
=
77
kip
Step 5 · Find governing (G)
Use G = the combination with the largest of U₁, U₂ and U₃
Live load is the bigger variable load, so the combination taking it at 1.6 governs.
77
≥
70,
77
≥
28:
1.2
D
+
1.6
L
+
0.5
S
G
=
the
combination
with
the
largest
of
28,
77
and
70
G
=
1.2
D
+
1.6
L
+
0.5
S
Check
Put the numbers back in. Both sides should match.
28 = 1.4 × 20 ✓
77 = 1.2 × 20 + 1.6 × 30 + 0.5 × 10 ✓
70 = 1.2 × 20 + 1.6 × 10 + 30 ✓
77 = max(28, 77, 70) ✓
77
≥
70,
77
≥
28,
so
1.2
D
+
1.6
L
+
0.5
S
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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