BIZOMAT 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. |
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: Beam
- What it is
- How the beam is held and where the falling mass strikes it: at mid-span of a beam resting on two supports, or at the free end of a cantilever fixed at one end.
- Units and format
- Choose one of 2 options from the list: Simply supported, load at mid-span; Cantilever, load at the free end.
- 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
- The model assumes the mass lands at mid-span or the cantilever tip; other impact points are not covered.
What this means: Falling mass
- What it is
- The mass of the object that falls onto the beam, such as a dropped load, tool or part.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg to 100000 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 stress and deflection rise in proportion; the impact factor also changes.
- Get it right
- Enter mass in kilograms; the tool converts it to weight.
What this means: Drop height
- What it is
- The height the mass falls freely before it first touches the beam.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 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 with it dynamic stress and deflection.
- Get it right
- Measure to the point of first contact, not to the floor below the beam.
What this means: Span (or cantilever length)
- What it is
- For a simply supported beam, the distance between the two supports; for a cantilever, the length from the fixed end to the point of impact.
- 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 2000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the clear span between support centres, not the overall length of the member.
What this means: Elastic modulus
- What it is
- The elastic (Young’s) modulus of the beam material, from the material data sheet or a materials reference.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 400 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 GPa, not MPa: the tool multiplies by 1000.
What this means: Second moment of area
- What it is
- The second moment of area of the beam cross-section about the bending axis, from a section table or the section geometry.
- 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 value for the axis the beam bends about; the strong and weak axes differ greatly. Convert cm⁴ by multiplying by 10 000.
What this means: Distance to the extreme fibre
- What it is
- The distance from the neutral axis of the section to the outermost fibre, where bending stress is highest. For a symmetrical section it is half the depth.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 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
- Stress is proportional to it.
- Get it right
- Measure from the neutral axis, not from the bottom of the section, for unsymmetrical shapes.
What this means: Allowable stress
- What it is
- The highest bending stress you will accept in the beam for this impact, from your design basis and the material properties. It also sets the largest safe drop height.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 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
- Decide whether the event is occasional or repeated; repeated impacts need a fatigue-based value.
What this means: Largest dynamic deflection allowed
- What it is
- The largest dynamic deflection of the beam you accept during the impact, set by clearances, attached equipment or function.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
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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Open the Drop Impact on a Beam (Impact Factor, Stress and Safe Drop Height) calculator