KEVOS® MAKEOS · Strength
Drop Impact on a Beam (Impact Factor, Stress and Safe Drop Height)
How much stress and deflection does a mass dropped on this beam cause, and from what height can it fall before the beam is overstressed?
Design check of a simply supported or cantilever beam struck by a falling mass: static deflection and stress under the weight, the impact factor 1 + √(1 + 2h ÷ δ_st), dynamic deflection and stress (as the beam impact tool), the equivalent static force, the energy absorbed (matching the impact load tool with the beam’s dynamic deflection as the stopping distance), and the largest drop height that keeps the stress within the allowable.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Beam | choice | How the beam is supported and where the mass lands. |
| Falling mass | kg | Mass that falls onto the beam. |
| Drop height | mm | Height the mass falls before touching the beam. |
| Span (or cantilever length) | mm | Span between supports, or length of the cantilever. |
| Elastic modulus | GPa | Elastic modulus of the beam. |
| Second moment of area | mm⁴ | Second moment of area of the section. |
| Distance to the extreme fibre | mm | Distance from the neutral axis to the extreme fibre. |
| Allowable stress | MPa | Allowable stress for impact (often up to yield for an occasional event; your value). |
| Largest dynamic deflection allowed | mm | Largest dynamic deflection you accept. |
Method and formulas
- Static deflection δ_st = W L³ ÷ 48EI (simply supported) or W L³ ÷ 3EI (cantilever); static stress from M = W L ÷ 4 or W L.
- Impact factor k = 1 + √(1 + 2h ÷ δ_st); dynamic stress and deflection = k × static (as the beam impact tool).
- Energy = W (h + δ_d) (as the impact load tool with δ_d as the stopping distance); equivalent static force = k W.
- Safe drop height h = δ_st [(k_a − 1)² − 1] ÷ 2 with k_a = allowable ÷ static stress.
- Example: 20 kg dropped 100 mm gives an impact factor of 99.946 and 61.258 MPa; it may fall up to 1,691.2 mm.
Limitations
- Elastic beam, mass stays in contact, beam mass neglected (conservative for heavy beams).
- Local crushing at the contact point is not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a beam or platform for dropped loads
- Find a safe drop height for a test rig
- Compare beam sections for impact
Who it is for
- Design engineers
- Structural engineers
- Safety engineers
What you get
- Static deflection, stress and impact factor
- Dynamic stress, deflection, equivalent force and energy
- Largest safe drop height
Interpreting the result
- A softer beam or a resilient pad lowers the impact factor: stiffness, not just strength, governs impact.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 278, 179–186. Topic reference; no source tables or recommended settings are reproduced.
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