Beam Load Calculator
Estimate maximum deflection, bending moment, and support shear for two simplified simply supported beam cases: a center point load or a uniform load over the full span. Assumptions are shown beside every result.
Point load
delta = P L^3 / 48 E I
Uniform load
delta = 5 w L^4 / 384 E I
Scope
Simple span only
Live calculator
Simple beam span, load, E, and I
Maximum deflection
1.757813 mm
Max moment
3,750 N m
Max shear
2,500 N
Span
3 m
Simply supported beam with a single center point load; small deflection, linear elastic behavior, constant E and I.
| Deflection in inches | 0.069205 in |
|---|---|
| Point load | 5,000 N |
| Uniform load | Not used |
| Max shear in lbf | 562.022358 lbf |
| Elastic modulus | 200 GPa |
Screen simple beam response with assumptions visible
Maximum deflection
Estimate midspan deflection for center point load or full-span uniform load cases.
Moment and shear
Calculate maximum bending moment and maximum shear from the selected load case.
Scope warning
Keep simple-span, linear-elastic, constant E and I assumptions visible beside the result.
Beam formulas used on this page
The calculator uses closed-form formulas for simple, simply supported beams under one basic load case at a time.
Working formulas
Center point load deflection
delta max = P L^3 / (48 E I)
Maximum deflection at midspan for a simply supported beam with center point load.
Uniform load deflection
delta max = 5 w L^4 / (384 E I)
Maximum deflection at midspan for a full-span uniform load.
Maximum moment
M max = P L / 4 or w L^2 / 8
The matching moment expression is selected from the chosen load case.
Symbols
- P - point load
- Concentrated load at span center.
- w - uniform load
- Distributed load over the full beam span.
- E - elastic modulus
- Material modulus in pascals after conversion.
- I - second moment of area
- Area moment of inertia in m^4 after conversion.
Beam results with the simplified case stated plainly
Closed-form beam checks
- The calculator supports center point load and uniform load over the full span.
- Span, load, elastic modulus, and second moment of area are converted before calculation.
- Deflection is shown in millimeters and inches for quick scale checks.
- Maximum moment and support shear are shown with the selected load case.
Assumptions are not hidden
- The result repeats that the model is simply supported, linear elastic, small deflection, and constant E and I.
- FAQ answers explain why complex supports, combined loads, code limits, and lateral stability are outside scope.
- Related links connect beam response to stress-strain checks and engineering note practices.
- The page is useful for learning and screening, not final structural design.
Beam load support for mechanics and design notes
Students
Check homework-scale examples while keeping formulas, SI conversions, and assumptions visible.
Design reviewers
Use quick preliminary checks before moving a problem into a full engineering workflow.
Worksheet builders
Create source-backed example rows with normalized units and clearly labeled outputs.
How it works in three quick steps.
Choose the load case
Select a simply supported center point load or full-span uniform load.
Enter span, load, E, and I
Add span length, load magnitude, elastic modulus, and second moment of area using the units you have.
Read deflection, moment, and shear
Review maximum deflection, maximum bending moment, maximum shear, and the simplified assumption note.
Save or print a beam load result
Copy the summary
Copy formula outputs and SI-normalized inputs into calculation notes or review comments.
Print the page
Print the calculator, formula notes, assumptions, FAQs, and related engineering links.
Document assumptions
Keep simplified scope notes beside the result before using values in a larger calculation.
Why beam calculators must state the load case
Beam formulas are easy to misuse because similar-looking diagrams can have different equations. Toolarithm's Beam Load Calculator limits the interactive model to two simple cases and labels the selected case beside the result. Center point load and full-span uniform load formulas are handled separately, with span, load, elastic modulus, and second moment of area normalized before output.
The calculator is not a structural design approval tool. It does not check code limits, combined loads, real support stiffness, notches, holes, lateral stability, material grade, connection details, or load duration. It is built for mechanics of materials examples, quick deflection scale checks, and documented calculation notes where assumptions need to be visible.
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