BuzCalculator

Structural Beam Load Capacity Calculator

Simply supported beam

Example input values for demonstrating the calculator. These custom properties and illustrative loads do not represent a verified beam or design load.

Load case
Unit system

Changing units preserves physical quantities. Invalid drafts remain invalid.

Span

Support-to-support span. Positive decimal; dot/comma accepted.

Uniform load

Full-span downward force per length. Zero is valid; lb means pound-force.

Use your own verified material and section properties. Changing the label does not assign E or strength values.

Elastic modulus E

Enter the actual elastic modulus for your material and project.

Moment of inertia I

I controls elastic deflection. Use the bending-axis second moment of area.

Section modulus S

S controls elastic bending stress: sigma = M/S. Use the elastic section modulus for the critical extreme fiber.

Entered bending-stress limit (optional)

Blank omits the bending comparison. Enter your project-specific comparison limit; no strength is assigned.

Deflection criteria vary by member function, finishes, loading type, jurisdiction, and design standard. Select the criterion appropriate to your project. L/360 is an example comparison criterion.

Enter the load case you want to analyze. This calculator does not create code load combinations. Include any self-weight in your entered load; no self-weight is added automatically.

BEAM ANALYSIS

Maximum bending moment

25,600 lb·ft

At midspan

Maximum shear force

6,400 lb

At supports; magnitude

Maximum deflection

1.1796 in

At midspan; downward

Maximum elastic bending stress

3,072 psi

Elastic extreme-fiber magnitude

Bending comparison

WITHIN ENTERED BENDING LIMIT

Utilization of entered bending limit: 76.8%

Deflection comparison

EXCEEDS SELECTED DEFLECTION LIMIT

Selected deflection limit: 0.53333 in

Utilization of selected deflection limit: 221.18%

Other structural limit states are not evaluated.

Left reaction
6,400 lb
Right reaction
6,400 lb

Structural note: This calculator applies simplified elastic beam formulas to the properties and limits you enter. It does not verify full structural capacity, code compliance, connections, stability, bearing, load combinations, or project-specific safety.

Verify loads, material/section properties, support conditions, and applicable design requirements before construction.

Load and deflection diagram

Simply supported beam, full-span distributed load, with schematic downward deflection800 lb/ftSpan: 16 ft
Simply supported beam. Uniform arrows cover the full span. Span 16 ft; load 800 lb/ft. Maximum moment and deflection occur at midspan; maximum shear magnitude at supports. Exaggerated elastic deflection shape for illustration. Not to scale.
Show calculations

Full precision SI normalization: N, m, Pa, m⁴, m³. Display rounding never determines comparisons.

  • Total load: W = wL = 12,800 lb
  • Support reactions: RA = RB = wL/2 = 6,400 lb each
  • Maximum shear: Vmax = wL/2 = 6,400 lb at supports
  • Maximum moment: Mmax = wL²/8 = 25,600 lb·ft at midspan
  • Maximum elastic bending stress: sigma = M/S = 3,072 psi
  • Maximum deflection: δ = 5wL⁴/(384EI) = 1.1796 in at midspan
  • Selected deflection limit: L/360 = 0.53333 in

Single span, simply supported beam, constant section, linear-elastic small-deflection Euler–Bernoulli analysis; one full-span uniform load or one center point load. Other structural limit states are not evaluated.

BEAM ANALYSIS
Simply supported beam
Full-span uniform load
Material label: Custom (properties user supplied)
span: 16 ft
uniformLoad: 800 lb/ft
E: 1000000 psi
I: 1000 in⁴
S: 100 in³
limit: 4000 psi
Total load: W = wL = 12,800 lb
Support reactions: RA = RB = wL/2 = 6,400 lb each
Maximum shear: Vmax = wL/2 = 6,400 lb at supports
Maximum moment: Mmax = wL²/8 = 25,600 lb·ft at midspan
Maximum elastic bending stress: sigma = M/S = 3,072 psi
Maximum deflection: δ = 5wL⁴/(384EI) = 1.1796 in at midspan
Selected deflection limit: L/360 = 0.53333 in
Left reaction = right reaction: 6,400 lb
WITHIN ENTERED BENDING LIMIT
EXCEEDS SELECTED DEFLECTION LIMIT
Utilization of entered bending limit: 76.8%
Utilization of selected deflection limit: 221.18%
Single span, simply supported beam, constant section, linear-elastic small-deflection Euler–Bernoulli analysis; one full-span uniform load or one center point load. Other structural limit states are not evaluated.
Structural note: This calculator applies simplified elastic beam formulas to the properties and limits you enter. It does not verify full structural capacity, code compliance, connections, stability, bearing, load combinations, or project-specific safety.

How to use

Estimate simply supported beam reactions, bending moment, shear force, elastic stress and deflection using user-entered properties.

  1. Choose Uniform Load or Center Point Load, then enter span and the already-combined load you want to analyze.
  2. Enter verified E, I and S for your bending axis. The material label changes guidance only; it never assigns stiffness or strength.
  3. Optionally enter a bending-stress limit. Choose a deflection criterion, including custom L/x.
  4. Read each comparison independently and review assumptions before using the results.

Structural note: This calculator applies simplified elastic beam formulas to the properties and limits you enter. It does not verify full structural capacity, code compliance, connections, stability, bearing, load combinations, or project-specific safety.

Simply supported beam model

Single span, simply supported beam, constant section, linear-elastic small-deflection Euler–Bernoulli analysis; one full-span uniform load or one center point load. Other structural limit states are not evaluated. A pin and roller idealization permits end rotation and produces no end moment. It does not describe fixed supports, cantilevers or continuous beams.

Small deflections, constant E and I, and transverse downward loading are assumed. Shear deformation and axial effects are omitted.

Uniformly distributed load

Uniform beam formulas

With span L and uniform load intensity w, total load W = wL. RA = RB = wL/2. Maximum shear magnitude Vmax = wL/2; maximum moment Mmax = wL²/8. Maximum downward elastic deflection δmax = 5wL⁴/(384EI).

Load covers the full span. Both moment and deflection peak at midspan.

Center point load

A single center point load P gives RA = RB = P/2; Vmax = P/2; Mmax = PL/4; δmax = PL³/(48EI).

Moment and deflection peak at midspan. The point force creates a shear jump at center.

Support reactions

Vertical equilibrium requires RA + RB = W. Symmetry makes the two upward reactions equal: wL/2 for UDL, P/2 for center load. These are forces, not bearing or connection capacities.

Maximum shear

Maximum shear-force magnitude is wL/2 or P/2. Its maximum occurs at supports; for the center load the same magnitude extends over each half-span. Arbitrary cross-section shear stress distribution is not calculated, and no shear capacity is inferred.

Maximum bending moment

Maximum bending moment is wL²/8 for full-span UDL and PL/4 for a center point load. Moment is force × length. Results use lb·ft or kN·m after consistent normalization.

Bending stress

sigma = M/S. The maximum elastic bending-stress magnitude is maximum moment divided by the elastic section modulus for the critical extreme fiber. Use matching bending-axis properties.

An optional entered bending-stress limit is a user-supplied comparison, not an automatically determined material strength. Utilization of entered bending limit = calculated stress / entered limit × 100%. Raw values determine WITHIN ENTERED BENDING LIMIT or EXCEEDS ENTERED BENDING LIMIT; blank produces NO BENDING LIMIT ENTERED.

Moment of inertia and section modulus

I is second moment of area (length⁴), not mass moment of inertia. It controls elastic deflection through EI. S is elastic section modulus (length³), S = I/c, used for sigma = M/S. For an asymmetric section, enter the section modulus for the governing extreme fiber.

The optional rectangular helper calculates I = bh³/12 and S = bh²/6. h is bending depth. Swapping width and depth changes these properties. The helper provides geometry only and never assigns material capacity.

Conversions raise the length factor to the fourth power for I and third power for S: in⁴ ↔ mm⁴ and in³ ↔ mm³.

Beam deflection

Maximum deflection is 5wL⁴/(384EI) or PL³/(48EI), at midspan. These small-deflection Euler–Bernoulli formulas omit shear deformation, creep and nonlinear response.

The diagram exaggerates a schematic elastic shape. It is not to scale and is not a construction drawing.

Deflection limits

Selected deflection limit = L / denominator. L/180, L/240, L/360, L/480 and custom L/x are comparison criteria. Default L/360 is an example criterion, not a universal code value.

Deflection criteria vary by member function, finishes, loading type, jurisdiction, and design standard. Select the criterion appropriate to your project.

Raw deflection is compared with L/x to show WITHIN SELECTED DEFLECTION LIMIT or EXCEEDS SELECTED DEFLECTION LIMIT. There is no overall combined conclusion.

Modeled bending/deflection thresholds

This calculator checks selected elastic bending and deflection criteria. Structural capacity requires additional limit states and project-specific design requirements.

V1 analyzes the entered load only. It does not solve maximum loads or show modeled load thresholds, recommend a standard beam, or choose a beam size. Separate analyses can be made by entering different custom properties; there is no automatic winner or multi-section comparison mode.

What this calculator does not check

Not evaluated: shear capacity, lateral-torsional buckling, local buckling, web crippling, bearing, seat length, bolts, welds, joist hangers, end connections, vibration, fire resistance, seismic performance, wind/snow load compliance, load combinations, code compliance, member sizing, allowable code span, construction safety or design approval. No verified section database or design-code tables are provided.

For roof dimensions, check common-rafter geometry separately. A rafter’s rise, run and slope do not establish load-bearing adequacy, member sizing, code compliance or permit approval.

Worked examples

1. Full-span uniform load, custom properties

Example input values for demonstrating the calculator. Span 16 ft; uniform load 800 lb/ft. E = 1000000 psi; I = 1000 in⁴; S = 100 in³. Entered bending limit 4000 psi; example criterion L/360.

  • Total load: W = wL = 12,800 lb
  • Support reactions: RA = RB = wL/2 = 6,400 lb each
  • Maximum shear: Vmax = wL/2 = 6,400 lb at supports
  • Maximum moment: Mmax = wL²/8 = 25,600 lb·ft at midspan
  • Maximum elastic bending stress: sigma = M/S = 3,072 psi
  • Maximum deflection: δ = 5wL⁴/(384EI) = 1.1796 in at midspan
  • Selected deflection limit: L/360 = 0.53333 in

WITHIN ENTERED BENDING LIMIT; EXCEEDS SELECTED DEFLECTION LIMIT. These comparisons do not establish structural adequacy.

2. Center point load, same custom properties

Example input values for demonstrating the calculator. Span 16 ft; center load 5000 lb. E = 1000000 psi; I = 1000 in⁴; S = 100 in³. Entered bending limit 4000 psi; example criterion L/360.

  • Total load: W = P = 5,000 lb
  • Support reactions: RA = RB = P/2 = 2,500 lb each
  • Maximum shear: Vmax = P/2 = 2,500 lb at supports
  • Maximum moment: Mmax = PL/4 = 20,000 lb·ft at midspan
  • Maximum elastic bending stress: sigma = M/S = 2,400 psi
  • Maximum deflection: δ = PL³/(48EI) = 0.73728 in at midspan
  • Selected deflection limit: L/360 = 0.53333 in

WITHIN ENTERED BENDING LIMIT; EXCEEDS SELECTED DEFLECTION LIMIT. These comparisons do not establish structural adequacy.

3. Example L/360 comparison

Using example 1, computed deflection 1.1796 in is compared against 0.53333 in. EXCEEDS SELECTED DEFLECTION LIMIT. L/360 is an example criterion.

Rectangular helper example: b = 4 in; h = 12 in bending depth. Engine-generated I = 576 in⁴; S = 96 in³.

4. Rectangular geometry, same illustrative E and load

Example input values for demonstrating the calculator. Span 16 ft; uniform load 800 lb/ft. E = 1000000 psi; I = 575.9999999999999 in⁴; S = 95.99999999999997 in³. Entered bending limit 4000 psi; example criterion L/360.

  • Total load: W = wL = 12,800 lb
  • Support reactions: RA = RB = wL/2 = 6,400 lb each
  • Maximum shear: Vmax = wL/2 = 6,400 lb at supports
  • Maximum moment: Mmax = wL²/8 = 25,600 lb·ft at midspan
  • Maximum elastic bending stress: sigma = M/S = 3,200 psi
  • Maximum deflection: δ = 5wL⁴/(384EI) = 2.048 in at midspan
  • Selected deflection limit: L/360 = 0.53333 in

WITHIN ENTERED BENDING LIMIT; EXCEEDS SELECTED DEFLECTION LIMIT. These comparisons do not establish structural adequacy.

5. Equivalent metric mechanics

Example input values for demonstrating the calculator. Span 4.876799999999999 m; uniform load 11.675122349765093 kN/m. E = 6894.757293168361 MPa; I = 416231425.59999996 mm⁴; S = 1638706.4 mm³. Entered bending limit 27.57902917267344 MPa; example criterion L/360.

  • Total load: W = wL = 56.937 kN
  • Support reactions: RA = RB = wL/2 = 28.469 kN each
  • Maximum shear: Vmax = wL/2 = 28.469 kN at supports
  • Maximum moment: Mmax = wL²/8 = 34.709 kN·m at midspan
  • Maximum elastic bending stress: sigma = M/S = 21.181 MPa
  • Maximum deflection: δ = 5wL⁴/(384EI) = 29.963 mm at midspan
  • Selected deflection limit: L/360 = 13.547 mm

WITHIN ENTERED BENDING LIMIT; EXCEEDS SELECTED DEFLECTION LIMIT. These comparisons do not establish structural adequacy.

Assumptions and limitations

Structural note: This calculator applies simplified elastic beam formulas to the properties and limits you enter. It does not verify full structural capacity, code compliance, connections, stability, bearing, load combinations, or project-specific safety.

Actual behavior can differ with yielding, cracking, creep, load duration, moisture, connections, composite action, support conditions and material nonlinearity. Wood properties depend on species, grade, size, moisture, duration, temperature, treatment, repetitive-member factors and design method; none are silently assumed or adjusted. Steel grades, strengths and stability are not assigned.

Enter the analysis load you want to examine. No self-weight is added. Dead/live combinations, tributary-area loads, occupancy, roof, snow and building load determination are outside this model. No AISC, NDS or Eurocode member-design rules are encoded.

Inputs stay in browser memory. No saved projects, input persistence or network calculations. Units are normalized to N, m, Pa, m⁴ and m³; comparisons use full precision while displayed values use sensible significant digits.

Verify loads, material/section properties, support conditions, and applicable design requirements before construction.

FAQ

How do I calculate beam bending moment?

For a full-span uniform load, maximum moment is wL²/8. For a center point load it is PL/4. Both maxima are at midspan in this simply supported model.

How do I calculate support reactions for a simply supported beam?

For these symmetric cases, both support reactions are half the total load: wL/2 for uniform load and P/2 for a center point load.

How do I calculate maximum beam deflection?

Use 5wL⁴/(384EI) for a uniform load or PL³/(48EI) for a center point load. Enter consistent units and bending-axis I. Both maxima occur at midspan.

What is the difference between moment of inertia and section modulus?

I is the second moment of cross-sectional area and controls elastic deflection. S is elastic section modulus, I/c, where c is the extreme-fiber distance; it converts moment into bending stress.

How do I calculate bending stress in a beam?

Maximum elastic bending stress is sigma = M/S, using the maximum moment and the elastic section modulus for the critical extreme fiber.

What does L/360 mean?

It compares computed deflection with span divided by 360. For a 16 ft span, the example criterion is 192/360 inches. It is a selected comparison, not a universal design requirement.

Can this calculator check a uniformly distributed load and a center point load?

Yes, one case at a time: a uniform load across the entire span or a single point load at midspan. Off-center, multiple, partial-span and moment loads are unsupported.

Does being within the entered bending limit mean the beam is structurally adequate?

No. The comparison only checks calculated elastic bending stress against the limit you entered. Structural adequacy requires other limit states and project-specific requirements.

Does this calculator check shear, buckling, bearing, or connections?

It calculates shear force only. It does not check shear stress or capacity, buckling, bearing, bolts, welds, joist hangers, seat length or connections.

Does this calculator determine code-compliant beam capacity or the beam size I should use?

No. It does not select a beam, establish code-compliant capacity, determine building loads, or verify construction safety. Verify loads, properties, supports and design requirements before construction.

Sources

Sources support mechanics and unit conventions; they do not endorse this calculator or a project design.