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

InputUnitTypical source
SupportchoiceSupport arrangement and impact point.
Falling masskgMass of the falling object.
Drop height above the beammmHeight it falls before touching the beam.
Span (or cantilever length)mmSpan, or cantilever length.
Elastic modulusGPaElastic modulus from the material data sheet (steel is typically about 200 GPa).
Second moment of areamm⁴Second moment of area of the beam section.
Distance to extreme fibremmNeutral axis to extreme fibre.
Allowable stressMPaAllowable 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
Illustration: SupportThe options for Support, with the one currently selected highlighted.Simply supported, load at mid-spanCantilever, load at the tipExample: Simply supported, load at…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
Illustration: Falling massA weight resting on a scale; Falling mass is how much matter it contains, in kilograms or grams.mExample: 20 kgFalling 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
Illustration: Drop height above the beamA block with a vertical dimension line from its base to its top, marking the height Drop height above the beam.hExample: 100 mmDrop 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)
Illustration: Span (or cantilever length)A bar with a dimension line and arrows from one end to the other, marking the length Span (or cantilever length).LExample: 2000 mmSpan (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
Illustration: Elastic modulusA stress against strain graph whose straight starting slope is the stiffness value Elastic modulus.stressstrainEExample: 200 GPaElastic 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
Illustration: Second moment of areaThe cross-section of a beam with its neutral axis; Second moment of area describes how the section’s area is spread around that axis.neutral axisIExample: 8000000 mm⁴Second 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
Illustration: Distance to extreme fibreA bar with a dimension line and arrows from one end to the other, marking the length Distance to extreme fibre.cExample: 50 mmDistance 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
Illustration: Allowable stressA test bar pulled from both ends: stress Allowable stress is the force carried by each square millimetre of its cross-section.σallstress = force ÷ areaExample: 250 MPaAllowable 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

  1. Static: simply supported δst = WL³ ÷ 48EI, M = WL/4; cantilever δst = WL³ ÷ 3EI, M = WL.
  2. Impact factor = 1 + √(1 + 2h ÷ δst).
  3. Dynamic deflection and stress = factor × static values.
  4. 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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