BIZOMAT MAKEOS · Engineering
Beam Stress and Deflection
What stress and deflection does this ideal beam model predict?
Screen a prismatic beam under one defined load case using supplied section properties and elastic modulus.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load case | choice | Match the actual support and load arrangement to one of these ideal cases. |
| Total applied load | N | Point force, or TOTAL uniformly distributed load over the entire span. |
| Span | mm | Support span, or fixed face to load for a cantilever. |
| Young’s modulus | MPa | Verified elastic modulus at the operating temperature. |
| Second moment of area | mm⁴ | Section property about the actual bending axis; do not use polar moment. |
| Extreme fibre distance | mm | Distance from the neutral axis to the most distant fibre. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Load case
- What it is
- The support and loading arrangement: a beam on two simple supports with one central point load, a cantilever with a point load at its free end, or simple supports with load spread evenly along the span.
- Units and format
- Choose one of 3 options from the list: Simply supported · central point load; Cantilever · tip point load; Simply supported · uniform load.
- Example
- The form opens with “Simply supported · central point load” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- For the same load and span, the cantilever case gives by far the largest deflection and moment.
- Get it right
- Real supports are rarely perfectly simple or fixed; choose the case closest to the actual arrangement.
What this means: Total applied load
- What it is
- The force acting on the beam: the single point force, or for the uniform load case the total of all the distributed load over the whole span.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N to 1000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Moment, stress and deflection are directly proportional to load.
- Get it right
- For a uniform load, enter the total force (load per metre times span), not the load per metre. Convert kg to N first.
What this means: Span
- What it is
- The distance between the two supports, or for a cantilever the distance from the fixed face to the point load.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Deflection rises with the cube of span: doubling it gives eight times the deflection.
- Get it right
- Measure between support centres, not the overall beam length.
What this means: Young’s modulus
- What it is
- The elastic (Young’s) modulus of the beam material: how stiff it is in tension and compression, from verified material data at the operating temperature.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.001 MPa to 10000000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200000 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Deflection is inversely proportional to modulus; stress does not change.
- Get it right
- Enter MPa, not GPa: 1 GPa is 1000 MPa.
What this means: Second moment of area
- What it is
- The second moment of area of the beam cross-section about the axis it bends around, from a section table or calculation.
- Units and format
- Enter a number in mm⁴: millimetres to the fourth power (second moment of area). The form accepts 0.000001 mm⁴ or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000000 mm⁴ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Deflection and stress are both inversely proportional to the second moment of area.
- Get it right
- Use the value for the actual bending axis (strong or weak), and not the polar moment J.
What this means: Extreme fibre distance
- What it is
- The distance from the neutral axis of the section to the outermost surface in the bending direction, where bending stress is highest.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bending stress is directly proportional to this distance; deflection does not change.
- Get it right
- For a symmetric section it is half the depth; for unsymmetric sections use the larger distance.
Method and formulas
- Simply supported central point: Mmax = F × L / 4; δmax = F × L³ / (48 × E × I).
- Cantilever tip point: Mmax = F × L; δmax = F × L³ / (3 × E × I).
- Simply supported uniform TOTAL load: Mmax = F × L / 8; δmax = 5 × F × L³ / (384 × E × I).
- Bending stress = Mmax × fibre distance / I. Example central point case: 1000 N, 1000 mm, E = 200000 MPa, I = 1000000 mm⁴, c = 50 mm gives 12.5 MPa and 0.104167 mm.
Limitations
- Linear elastic, small-deflection Euler–Bernoulli model; shear deflection and support flexibility excluded.
- No strength rating, buckling, fatigue, connection, impact or code-compliance assessment.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- beam bending
- stiffness
- deflection
Who it is for
- Mechanical designers
- Fixture designers
What you get
- Maximum bending moment
- Maximum nominal bending stress
- Maximum deflection
- Deflection / span
Interpreting the result
- Compare against project-specific allowables and verify that the ideal supports match the real load path.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 232–244, 256–273. Topic reference; no source tables or recommended settings are reproduced.
- MIT OpenCourseWare, David Roylance: Beam Displacements — https://ocw.mit.edu/courses/3-11-mechanics-of-materials-fall-1999/resources/mit3_11f99_bdisp/
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Spring elements: what is inside a load cell
In Strain Gauges and Load Cells by the Numbers
What it covers: How column, bending-beam, double-bending and shear-beam load cells turn force into strain, how load position affects them, and how to estimate a spring element's strain and stress.
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