BIZOMAT MAKEOS · Strength
Impact Load on a Beam
What stress and deflection does a dropped weight cause in this beam?
Static deflection, impact factor, dynamic deflection and dynamic bending stress when a weight falls onto a simply supported beam at mid-span or onto a cantilever tip.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Support | choice | Support arrangement and impact point. |
| Falling mass | kg | Mass of the falling object. |
| Drop height above the beam | mm | Height it falls before touching the beam. |
| Span (or cantilever length) | mm | Span, or cantilever length. |
| Elastic modulus | GPa | Elastic modulus from the material data sheet (steel is typically about 200 GPa). |
| Second moment of area | mm⁴ | Second moment of area of the beam section. |
| Distance to extreme fibre | mm | Neutral axis to extreme fibre. |
| Allowable stress | MPa | Allowable stress for this (often accidental) load case. |
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: Support
- What it is
- How the beam is held and where the weight lands: on a simply supported beam at mid-span, or on the free tip of a cantilever.
- Units and format
- Choose one of 2 options from the list: Simply supported, load at mid-span; Cantilever, load at the tip.
- Example
- The form opens with “Simply supported, load at mid-span” selected as a worked example. Choose the option that matches your case.
- Get it right
- Pick the case that matches the real supports; a cantilever deflects much more than a simply supported beam of the same span.
What this means: Falling mass
- What it is
- The mass of the object that falls onto the beam; the tool converts it to a weight with standard gravity.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg to 10000000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Static deflection and stress rise in proportion to mass; dynamic stress rises too, though less than proportionally.
- Get it right
- Enter kilograms, not newtons.
What this means: Drop height above the beam
- What it is
- The free fall height from the underside of the object to the top of the beam, before contact.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher drop raises the impact factor and so the dynamic deflection and stress.
- Get it right
- Measure the fall before contact only; zero height still gives an impact factor of two for a suddenly applied load.
What this means: Span (or cantilever length)
- What it is
- The distance between the two supports of a simply supported beam, or from the fixed end to the tip of a cantilever.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Static deflection grows with the cube of the span and moment with the span, so longer beams are softer and more highly stressed.
What this means: Elastic modulus
- What it is
- The elastic (Young’s) modulus of the beam material, which with the second moment of area sets the beam’s stiffness.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter gigapascals, not megapascals.
What this means: Second moment of area
- What it is
- The second moment of area of the beam section about the bending axis, from section tables or a section 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 8000000 mm⁴ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the axis that bends under the falling load, normally the strong axis of a beam on its edge.
What this means: Distance to extreme fibre
- What it is
- The distance from the neutral axis of the beam to the outermost fibre, used to turn the bending moment into stress.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 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.
- Get it right
- For a symmetrical section this is half the depth.
What this means: Allowable stress
- What it is
- The highest bending stress you accept for this impact case; the dynamic stress is compared with it.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Impact is often an accidental load case; use the allowable your code gives for that case.
Method and formulas
- Static: simply supported δst = WL³ ÷ 48EI, M = WL/4; cantilever δst = WL³ ÷ 3EI, M = WL.
- Impact factor = 1 + √(1 + 2h ÷ δst).
- Dynamic deflection and stress = factor × static values.
- Example: 20 kg dropped 100 mm on the default beam gives an impact factor of 99.946 and 61.258 MPa.
Limitations
- The beam mass and local indentation are ignored (conservative for light beams, less so for heavy ones).
- Elastic response assumed; above yield the energy is absorbed plastically.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check guards, stops and platforms against dropped objects
- Estimate shock loading on a beam
- Compare stiff and flexible supports
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Static deflection and stress
- Impact factor
- Dynamic deflection and stress
Interpreting the result
- A more flexible beam has a lower impact factor; a stiff beam sees higher dynamic stress.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 278. Topic reference; no source tables or recommended settings are reproduced.
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