The lightest AISC W-shape that carries a uniformly loaded simple span in flexure, shear and deflection, by LRFD or ASD, with the next heavier options that also work.
AISC 360-16
Basis
Span and loads
Limits
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W14x22 · 22 lb/ft · governed by deflection
Section — W14x22
22
Depth
13.70 in
Live-load deflection
0.65 in
Total-load deflection
1.16 in
Heavier options that also work
Sometimes the lightest section is not the one you want — a shallower beam buys headroom, a deeper one buys stiffness.
Section
lb/ft
d (in)
Worst DCR
W12x26
26
12.2
0.79
W14x26
26
13.9
0.66
W16x26
26
15.7
0.56
Needs Zx ≥ 24.6 in³ and Ix ≥ 161 in⁴ · strength alone: W12x19 · stiffness alone: W14x22
Design checks
Check
Demand
Capacity
DCR
Status
Flexure
92.160 kip·ft
124.500 kip·ft
0.740
✓ OK
Shear
15.360 kip
94.530 kip
0.162
✓ OK
Live-load deflection (L/360)
0.647 in
0.800 in
0.808
✓ OK
Calculation
1Factored design loadASCE 7, document reference
w_u = 1.2D + 1.6L
w = 1.280
w_u=1.280 kip/ft
2Moment and shear on a simple span
M = \frac{wL^2}{8}, \quad V = \frac{wL}{2}
M = 92.2, \quad V = 15.4
M_u=92.2 kip·ft
3Plastic modulus requiredAISC360 F2.1
Z_{x,req} = \frac{M_u}{\phi_b F_y}
Z_{x,req} = 24.600 \text{ in}^3
Z_{x,req}=24.6
φb = 0.9, Fy = 50 ksi.
4Second moment of area required for the deflection limit
Unfactored live load. Deflection is a serviceability question, so the load factors do not apply to it.
Notes
Deflection governs. The section is stronger than it needs to be, and stiffness is what set its size — a shallower, heavier shape will not help.
Strength alone would allow W12x19 at 19 lb/ft. The deflection limit is what pushed the selection to W14x22.
Assumptions
Simply supported, single span, uniformly loaded.
The compression flange is continuously braced, so the shape reaches its plastic moment.
The section is compact for flexure, which every rolled W-shape in this table is at the grades offered.
Deflection is checked on the unfactored live load against the stated limit, and the total load is reported alongside it.
What this calculator does not check
Selects a section. It does not design the connections, the bearing, the web at a point load, or any stiffener.
No lateral-torsional buckling. An unbraced or partially braced beam has a lower capacity than this reports, and is out of scope.
No check on web crippling or web yielding under a concentrated load or at a support.
No camber, vibration or floor-response check. A long-span floor beam that satisfies L/360 can still be unacceptably lively.
The shape table covers W8 to W30 up to 99 lb/ft only. A heavier or deeper section is not considered even if it would be the right answer.
Self-weight is reported but not added to the demands, matching the source tool. Include it in the dead load if it matters.
Results are for preliminary sizing and educational use. They are not a design and must be reviewed, verified and sealed by a licensed or registered engineer before being used in construction.