What is the deflection limit for a floor beam per building code?

Per IBC 2024 Table 1604.3, floor beams supporting live load must not deflect more than L/360, where L is the span length in inches. For total load (dead + live), the limit is L/240. Beams supporting brittle finishes such as tile or plaster have a more stringent live-load limit of L/480.

What is the modulus of elasticity for steel beams?

Structural steel has a modulus of elasticity (E) of 29,000,000 psi (29,000 ksi) per AISC Steel Construction Manual, 16th Edition. This value is constant for all ASTM A36, A572, and A992 steel grades used in structural framing.

How is beam deflection calculated for a simply supported beam with a center point load?

Maximum deflection at midspan equals (P × L³) / (48 × E × I), where P is the applied load in pounds, L is the span in inches, E is the modulus of elasticity in psi, and I is the moment of inertia in in⁴. This formula is from AISC Manual Table 3-22 and applies when the load is located at the exact center of a simply supported beam.

What is the deflection formula for a cantilever beam with a point load at the free end?

For a cantilever beam with a concentrated load at the free end, maximum deflection equals (P × L³) / (3 × E × I). Cantilevers deflect significantly more than simply supported beams of the same span because the fixed end provides only one reaction point, per Roark's Formulas for Stress and Strain, 8th Edition, Table 8.1.

What causes excessive beam deflection in concrete construction?

Excessive deflection in concrete beams is most commonly caused by undersizing the moment of inertia, selecting too low a concrete compressive strength (f'c), or ignoring long-term creep effects. ACI 318-19 Section 24.2.2 requires that calculated deflections account for the effects of sustained loads over time, which can increase deflection by a factor of 2 or more.

How do I find the moment of inertia for an I-beam or W-shape?

Moment of inertia values for standard AISC W-shapes are listed in AISC Steel Construction Manual Table 1-1. For example, a W8x31 has Ix = 110 in⁴ about the strong axis. For a rectangular section, I = (b × h³) / 12, where b is width and h is depth. This calculator includes a built-in W-shape lookup for common sections.

What is the modulus of elasticity for concrete beams?

Per ACI 318-19 Section 19.2.2.1, the modulus of elasticity for normal-weight concrete is Ec = 57,000 × √f'c (psi), where f'c is the 28-day compressive strength in psi. For 4,000 psi concrete, Ec ≈ 3,605,000 psi. This is substantially lower than steel, making concrete beams much more flexible for a given cross-section.

Beam Deflection Calculator - Simply Supported, Cantilever & Fixed Beams

📈 Beam Deflection Calculator

Enter your beam geometry, load, and section properties below. All required fields are marked *.

Beam Support Type * Select how your beam is supported at each end.

Load Configuration * Choose the load distribution applied to the beam.

Load Position from Left Support (ft) *

ft

Must be less than beam span.

Beam Span (ft) *

ft

Clear span between supports, 0.5–300 ft.

Point Load (lb) *

lb

Total point load or load per linear foot for UDL.

Material * Material sets the elastic modulus (E). Select "Custom" to enter a specific value.

Modulus of Elasticity, E (psi) *

psi

Steel: 29,000,000 psi. Concrete f'c 4,000 psi: 3,605,000 psi. Douglas Fir: 1,700,000 psi.

Section Properties * Select a standard W-shape or lumber section, or enter moment of inertia manually.

Moment of Inertia, I (in⁴) *

in⁴

Found in AISC Manual Table 1-1 for W-shapes, or calculate as (b × h³) / 12 for rectangles.

Application Type * Sets the IBC 2024 Table 1604.3 deflection limit for pass/fail check.

Display Units

Results are for planning and preliminary design only. Structural members in permitted construction must be verified by a licensed engineer. See full disclaimer below.

How the Beam Deflection Calculator Works

⎳

Choose Support Conditions

Select simply supported, cantilever, or fixed-fixed. Each condition produces a different deflection equation and reaction force distribution.

⇣

Define the Load

Enter a point load at midspan or any position, or a uniformly distributed load in lb/ft. Add self-weight for total-load deflection checks.

▊

Select Material and Section

Pick from steel (E = 29,000,000 psi), concrete, or wood presets, or enter a custom modulus. Use the W-shape database for standard steel sections.

✓

Read Code Compliance Results

The calculator applies IBC 2024 Table 1604.3 limits and returns pass/fail status, demand-to-capacity ratio, and maximum bending moment.

IBC 2024 Allowable Deflection Limits — Table 1604.3

The International Building Code sets maximum deflection limits based on element type and load case. These limits protect finishes, prevent occupant discomfort, and avoid damage to supported elements. The slab load calculator uses the same reference table for two-way slab checks.

IBC 2024 Table 1604.3 — Maximum Allowable Beam Deflection
Structural Element	Load Case	Limit	Example: 20 ft Span
Floor beams	Live load only (L)	L/360	0.667 in
Floor beams	Total load (D + L)	L/240	1.000 in
Roof beams	Live load only (L)	L/360	0.667 in
Roof beams	Total load (D + L)	L/240	1.000 in
Beams with brittle finishes (tile, plaster)	Live load only (L)	L/480	0.500 in
Cantilever beams	Live load only (L)	L/180	1.333 in (10 ft cant.)
Residential floors (IRC)	Live load only (L)	L/360	0.667 in

Source: IBC 2024 Table 1604.3. Spans are measured center-to-center of supports. For steel members, dead load deflection is set to zero per Table 1604.3 footnote g.

Beam Deflection Formulas Used in This Calculator

All deflection equations follow standard structural engineering references including AISC Steel Construction Manual Table 3-22 and Roark's Formulas for Stress and Strain, 8th Edition. For concrete beam design, refer to our concrete flexural strength calculator and the concrete modulus of elasticity calculator.

Simply Supported — Point Load at Center

δ_max = PL³ / (48EI)

M_max = PL / 4

AISC Table 3-22a, Case 1

Simply Supported — Uniform Distributed Load

δ_max = 5wL⁴ / (384EI)

M_max = wL² / 8

AISC Table 3-22a, Case 2

Cantilever — Point Load at Free End

δ_max = PL³ / (3EI)

M_max = PL

Roark's 8th Ed., Table 8.1

Cantilever — Uniform Distributed Load

δ_max = wL⁴ / (8EI)

M_max = wL² / 2

Roark's 8th Ed., Table 8.1

Fixed-Fixed — Point Load at Center

δ_max = PL³ / (192EI)

M_max = PL / 8

Roark's 8th Ed., Table 8.2

Fixed-Fixed — Uniform Distributed Load

δ_max = wL⁴ / (384EI)

M_max = wL² / 12

Roark's 8th Ed., Table 8.2

Where: δ_max = maximum deflection (in), P = point load (lb), w = distributed load (lb/in), L = span (in), E = modulus of elasticity (psi), I = moment of inertia (in⁴), M = bending moment (lb-in).

What Is Beam Deflection and Why Does It Matter?

Beam deflection is the vertical displacement of a structural beam under applied loads. Every beam deflects when loaded; the question is whether that deflection exceeds the limit that causes serviceability problems.

Excessive deflection causes cracked plaster, sticking doors, sloped floors, and visible sagging that makes occupants uncomfortable. In severe cases it can damage supported partitions, tile finishes, and mechanical systems. For structural adequacy, see the concrete load-bearing capacity calculator and the concrete stress calculator for combined stress checks.

Three variables control deflection: span length (L), load magnitude, and flexural stiffness (EI). Span length has the greatest impact because deflection scales with L to the third or fourth power. Doubling a beam's span increases deflection by 8x for a point load and 16x for a distributed load, at the same load intensity.

Elastic Modulus (E) by Material

Modulus of Elasticity (E) for Common Structural Materials
Material	E (psi)	E (ksi)	Standard
Structural Steel (A36, A572, A992)	29,000,000	29,000	AISC SCM 16th Ed.
Concrete, f'c = 3,000 psi	3,122,000	3,122	ACI 318-19 §19.2.2.1
Concrete, f'c = 4,000 psi	3,605,000	3,605	ACI 318-19 §19.2.2.1
Douglas Fir-Larch, No. 2	1,700,000	1,700	NDS 2018 Supplement Table 4A
Southern Pine, No. 2	1,600,000	1,600	NDS 2018 Supplement Table 4B
Glulam / LVL (typical)	1,800,000	1,800	NDS 2018 Supplement Table 5A

Sample Deflection Calculations

These worked examples follow the formulas in AISC Table 3-22 and IBC 2024 Table 1604.3. For rebar sizing in concrete beams, the rebar spacing calculator handles that step separately.

Example 1 — Steel Floor Beam, Simply Supported

Span	20 ft
Load	8,000 lb point load at center
Section	W14x34 (Ix = 340 in⁴)
Material	Structural Steel (E = 29,000,000 psi)
Application	Floor — Live Load (L/360)

δ_max = 0.394 in

Calculation: (8,000 × 240³) / (48 × 29,000,000 × 340) = 0.394 in. Allowable = 240 / 360 = 0.667 in. PASS (D/C = 0.59).

Example 2 — Cantilever Wood Beam

Span	8 ft
Load	600 lb/ft uniform distributed
Section	6x12 Lumber (Ix = 697 in⁴)
Material	Douglas Fir (E = 1,700,000 psi)
Application	Roof — Live Load (L/360)

δ_max = 0.711 in

Calculation: (600/12 × 96⁴) / (8 × 1,700,000 × 697) = 0.711 in. Allowable = 96 / 180 = 0.533 in (cantilever uses L/180). FAILS — upsize section or shorten span.

Example 3 — Concrete Beam, Fixed-Fixed

Span	24 ft
Load	1,200 lb/ft uniform distributed
Section	12 in × 24 in rectangle (Ix = 13,824 in⁴)
Material	Concrete f'c 4,000 psi (E = 3,605,000 psi)
Application	Floor — Total Load (L/240)

δ_max = 0.341 in

Calculation: (1,200/12 × 288⁴) / (384 × 3,605,000 × 13,824) = 0.341 in. Allowable = 288 / 240 = 1.200 in. PASS (D/C = 0.28). Note: Long-term creep per ACI 318-19 §24.2.4 may increase this by up to 2x under sustained loads.

Common Beam Deflection Calculation Errors

❌ Using feet instead of inches for span in the formula

The deflection formulas require L in inches. A 20 ft span is 240 inches. Entering 20 directly into the formula understates deflection by a factor of 1,728 (20³ = 8,000 vs. 240³ = 13,824,000). This calculator handles the conversion automatically.

❌ Ignoring beam self-weight as a distributed load

A W14x48 steel beam weighs 48 lb/ft. Over a 30 ft span, that adds 1,440 lb of dead load that many calculators omit. Per AISC Code of Standard Practice Section 3.1.2, self-weight must be included in total-load deflection checks.

❌ Using gross section (Ig) for cracked concrete beams

ACI 318-19 Section 24.2.3.5 requires using the effective moment of inertia (Ie) for cracked concrete beams under service loads. Using Ig overstates stiffness and understates deflection, often by 40-60%. This matters most for lightly reinforced sections.

❌ Applying the wrong formula for the support condition

A cantilever with a point load at the free end deflects 16 times more than a simply supported beam of the same span and load, because the formula coefficient changes from 1/48 to 1/3. Misidentifying the support condition is the most frequent input error.

❌ Omitting long-term creep in concrete

ACI 318-19 Section 24.2.4 requires that total deflection (including long-term creep) be compared to the L/240 or L/480 limit. The creep multiplier ranges from 1.2 to 2.0 depending on the compression reinforcement ratio. Checking elastic deflection alone against L/240 is not code-compliant for concrete.

Design tip: For steel floor beams, the AISC recommends pre-setting camber equal to 75% of the calculated dead-load deflection on beams longer than 20 ft (AISC Code of Standard Practice, Section 6.1). Use the camber field in Advanced Options to see the net deflection under live load only.

Frequently Asked Questions

What is the allowable deflection for a 20-foot floor beam? +

Per IBC 2024 Table 1604.3, the live-load deflection limit for a 20 ft floor beam is L/360 = (20 × 12) / 360 = 0.667 inches. The total-load limit is L/240 = 1.000 inch. If the beam supports a brittle finish such as ceramic tile, the live-load limit tightens to L/480 = 0.500 inches.

How much stiffer is a fixed-fixed beam compared to a simply supported beam? +

A fixed-fixed beam is 4 times stiffer than a simply supported beam under a center point load. The simply supported formula is PL³/(48EI) while the fixed-fixed formula is PL³/(192EI). For a uniformly distributed load, the fixed-fixed beam is also 4 times stiffer. This is why fixing a beam at both ends dramatically reduces midspan deflection.

Does increasing the beam depth reduce deflection more than increasing width? +

Yes. For a rectangular section, moment of inertia I = bh³/12. Depth (h) appears cubed, so doubling depth increases I by a factor of 8. Doubling width only doubles I. For this reason, deep narrow beams are far more efficient at controlling deflection than shallow wide beams of the same cross-sectional area.

What is the modulus of elasticity for a concrete beam with 4,000 psi compressive strength? +

Per ACI 318-19 Section 19.2.2.1, Ec = 57,000 × √f'c for normal-weight concrete (approximately 145 pcf). For f'c = 4,000 psi: Ec = 57,000 × √4,000 = 57,000 × 63.25 = 3,605,000 psi (3,605 ksi). This is about 8 times lower than structural steel's 29,000 ksi, which is why concrete beams require larger sections for equivalent stiffness.

What is beam camber and when should I use it? +

Camber is an intentional upward bow built into a beam to counteract anticipated dead-load deflection. Per AISC Code of Standard Practice Section 6.1, minimum camber is 75% of the calculated dead-load deflection for beams longer than 20 ft. After dead loads are applied, the beam deflects to near-flat, and the remaining deflection budget is then available for live load. Camber does not increase stiffness; it shifts the deflection baseline upward.

Can I use this calculator for a continuous multi-span beam? +

This calculator covers single-span beams: simply supported, cantilever, and fixed-fixed. Multi-span continuous beams require more complex analysis involving compatibility equations or the three-moment theorem. As a conservative estimate, treat each span as simply supported and add 15-20% for continuity effects. For multi-span concrete beams, ACI 318-19 permits using the gross section Ig with span length L taken as the center-to-center distance of supports.

How does the calculator handle point loads not at the center of a simply supported beam? +

For an eccentric point load at distance 'a' from the left support on a simply supported beam, the maximum deflection is Pa²b² / (3EIL) where b = L - a (per AISC Table 3-22a). The maximum deflection occurs at x = √((L² - b²)/3) from the left support when a > b. Select "Point Load — Any Position" and enter the distance from the left support to use this formula.

Sources and Methodology

AISC Steel Construction Manual, 16th Edition (2022) — Table 3-22 (beam diagrams and formulas), Table 1-1 (W-shape section properties). aisc.org/manual
ACI 318-19 — Building Code Requirements for Structural Concrete — Section 19.2.2.1 (modulus of elasticity for concrete), Section 24.2 (deflection calculations and limits). concrete.org
IBC 2024 — International Building Code — Table 1604.3 (allowable deflection of structural members). iccsafe.org
Roark's Formulas for Stress and Strain, 8th Edition (2012) — Table 8.1 (cantilever beams), Table 8.2 (fixed-fixed beams). Warren Young, Richard Budynas, Ali Sadegh.
NDS 2018 — National Design Specification for Wood Construction — Supplement Table 4A/4B (reference design values for sawn lumber). awc.org
AISC Code of Standard Practice for Steel Buildings and Bridges, 10th Edition (2022) — Section 6.1 (camber requirements). aisc.org

Last reviewed: May 2026. Built by Muhammad Ramzan Babar, physics researcher (PhD candidate). Reviewed by site author.

⚠ Engineering Disclaimer

This calculator provides estimates for planning purposes. For permitted structural work, foundations, multi-story construction, retaining walls over 4 feet, and commercial projects, calculations must be verified by a licensed structural engineer per IBC 2024 Section 1604. ConcreteCalculate.com is not liable for structural decisions made from these estimates.

Concrete beam deflection results do not account for long-term creep per ACI 318-19 Section 24.2.4. Multiply calculated deflection by the ACI creep factor (1.2 to 2.0) for total long-term deflection.

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Beam Deflection Calculator — Simply Supported, Cantilever & Fixed Beams