Beam size calculator

Flush Beam Substitution

Find a shallower steel beam that fits inside the floor and still carries the load. Answer the questions; the answer updates as you go.

1The beam on the drawings

The engineer's beam is the yardstick. The calculator checks it under the same loads so you can see how hard it is actually working.

Specified beamW12x40: 11 7/8" deep, 40 lb/ft

Span between supports

ftin

Center of bearing to center of bearing

Only show beams with equal or greater I_x and Z_xThe replacement must match or beat the specified beam's moment of inertia and plastic section modulus about the strong (x) axis

2Room for the beam

A flush beam has to fit within the floor framing. The beam can be no deeper than the joists, minus anything that sits on top of the steel.

Floor joist depth

Deepest beam allowed

Subtract a nailer or shim that sits on the beam, e.g. 1 1/2" for a 2x

Beam depths to consider

Anything that fitsW8 onlyW10 only

3Is the top of the beam braced?

An unbraced beam can roll sideways and buckle long before it bends. Joists or blocking fastened to the beam hold the top flange in place.

Braced by joists or blocking at a spacingJoist hangers or blocking attached to the beam on both sidesin apartBraced along its full lengthSubfloor fastened to a nailer bolted down the whole top flangeNot braced between supportsNothing attached to the beam between the two ends

4What the beam carries

Use the floor loads when you know the joist spans. If you don't, size the new beam to carry everything the specified beam could carry.

Use the floor loadsMost accurate, and usually allows a lighter beamMatch the specified beam's capacityConservative when the loads are unknown; point loads are ignored

Joists frame into the beam from

Both sidesOne side

Joist span, side A

Joist span, side B

Floor use

Dead / live

/psf

Wall or other load along the beam

deadlive, lb/ft

A wall above is about 10 psf of wall area: an 8 ft wall adds 80 lb/ft dead

Point loadsPosts or beams from above that land on this beam

Each foot of beam picks up 14.0 ft of floor: 210 lb/ft dead + 560 lb/ft live, plus the beam's own weight.

5Stiffness, ends and steel

Deflection limits keep the floor from feeling bouncy and protect finishes. Building codes require at least L/360 for live load on floors.

Live load deflection

Total load deflection

How the beam ends are supported

Sits on a post, column or pocketChecks the beam web for crushing over the supportBearing lengthinBolted or welded end connectionsThe connection is designed separately

Steel

Bearing width of posts above

Used for point loads

No single beam fits

Nothing 9 7/8" deep or less matches the W12x40

The W12x40 has I_x 307 in⁴ and Z_x 57 in³. The stiffest beam that fits is the W8x67 at I_x 272 (89%) and Z_x 70.1 (123%). Untick the I_x and Z_x rule in step 1 to size by the actual loads instead.

Two W10x33 beams side by side work (16% used each; together I_x 342 in⁴ (111%) · Z_x 77.6 in³ (136%) of the W12x40), if they are bolted together with spacers and both share the load equally. Other options: add a post to shorten the span, let the beam drop below the joists, or ask the engineer about a steel flitch plate.

Design numbers for the specified W12x40

Span: 16'-0"
Bending, factored: 38.3 k-ft of 213.8
Shear, factored: 9.6 k of 105.3
Live deflection: 0.09" max 0.53"
Total deflection: 0.13" max 0.80"
Steel: A992 50 ksi
Unbraced length: 16"
Left support: 1,680 D + 4,480 L lb
Right support: 1,680 D + 4,480 L lb

Support loads are service loads for sizing the posts and footings.

The specified W12x40 under the same loads

Uses 18% of its capacity, limited by bending strength. Bending strength 18%.I_x 307 in⁴ · Z_x 57 in³Live deflection 0.09", total 0.13".

The W12x40 has a lot of reserve on these loads, which is why a shallower beam can work. Confirm with the engineer that no other loads (roof, point loads, future use) were part of the original design.

Every beam that fits 9 7/8"

Beam	Depth	I_x in⁴	Z_x in³	Bending	Shear	Live defl.	Total defl.	Web	Result
W6x8.5	5 13/16"	14.9	5.73	177%	31%	358%	332%	30%	No, I_x/Z_x too low
W6x9	5 7/8"	16.4	6.23	159%	31%	326%	302%	31%	No, I_x/Z_x too low
W8x10	7 7/8"	30.8	8.87	113%	23%	173%	161%	37%	No, I_x/Z_x too low
W6x12	6"	22.1	8.3	120%	22%	242%	225%	17%	No, I_x/Z_x too low
W10x12	9 7/8"	53.8	12.6	79%	17%	99%	92%	33%	No, I_x/Z_x too low
W4x13	4 3/16"	11.3	6.28	158%	27%	472%	440%	13%	No, I_x/Z_x too low
W8x13	8"	39.6	11.4	87%	17%	135%	126%	20%	No, I_x/Z_x too low
W6x15	6"	29.1	10.8	98%	23%	183%	171%	17%	No, I_x/Z_x too low
W8x15	8 1/8"	48	13.6	73%	16%	111%	104%	19%	No, I_x/Z_x too low
W5x16	5"	21.4	9.63	103%	26%	249%	233%	15%	No, I_x/Z_x too low
W6x16	6 1/4"	32.1	11.7	85%	19%	166%	156%	15%	No, I_x/Z_x too low
W8x18	8 1/8"	61.9	17	59%	17%	86%	81%	22%	No, I_x/Z_x too low
W5x19	5 1/8"	26.3	11.6	86%	22%	203%	191%	13%	No, I_x/Z_x too low
W6x20	6 3/16"	41.4	14.9	67%	19%	129%	121%	14%	No, I_x/Z_x too low
W8x21	8 1/4"	75.3	20.4	49%	15%	71%	67%	19%	No, I_x/Z_x too low
W8x24	7 15/16"	82.7	23.1	43%	16%	65%	61%	19%	No, I_x/Z_x too low
W6x25	6 3/8"	53.4	18.9	53%	15%	100%	95%	11%	No, I_x/Z_x too low
W8x28	8 1/16"	98	27.2	37%	14%	54%	52%	15%	No, I_x/Z_x too low
W8x31	8"	110	30.4	33%	14%	49%	46%	14%	No, I_x/Z_x too low
W10x33	9 3/4"	171	38.8	26%	11%	31%	30%	15%	No, I_x/Z_x too low
W8x35	8 1/8"	127	34.7	29%	13%	42%	40%	12%	No, I_x/Z_x too low
W8x40	8 1/4"	146	39.8	26%	11%	37%	35%	9%	No, I_x/Z_x too low
W8x48	8 1/2"	184	49	21%	9%	29%	28%	8%	No, I_x/Z_x too low
W8x58	8 3/4"	228	59.8	17%	7%	23%	23%	6%	No, I_x/Z_x too low
W8x67	9"	272	70.1	15%	6%	20%	20%	5%	No, I_x/Z_x too low

Red I_x or Z_x is below the W12x40 (307 in⁴, 57 in³). Percent of capacity used. Green is under 50%, yellow is 50% or more (alert, marked ⚠), red is over 100% and fails. Sorted lightest first.

Confirm with the engineer of record

Any change to a specified beam needs the engineer's written approval before ordering.
This checks a single simple span. It does not cover continuous or cantilevered beams, connections, posts, footings, fire rating or floor vibration.
Ask the engineer which loads the W12x40 was sized for: roof or snow from above, walls, posts, and any future use.

2 × W10x33 two beams side by side

See why

Calculations follow AISC 360-16 (LRFD) for simply supported W shapes, with AISC v15.0 section properties. This is a preliminary sizing tool. A beam substitution must be approved by the engineer of record before it is ordered or installed.

Once your engineer signs off on the size, we can cut, drill and deliver the beam, or set it for you. Send us the size and length.

Send it for a price

Have drawings? Send them over for a quote.

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