KEVOS® MAKEOS · Strength
Shock Stress in Beams and Springs (Dropped Weight or Moving Body, Impact Factor, Allowable)
If a weight drops onto my beam or spring, or a moving body runs into it, what peak stress does the shock produce and is it within my allowable stress?
Stress produced by a shock load by the handbook formulas: a weight dropped through a height onto a simply supported beam at its centre, a cantilever at its free end, a beam fixed at both ends at its centre, or a helical spring of round or square wire; the static stress and deflection under the weight, the stress from the full formula p = p_s(1 + √(1 + 2h ÷ y)) and the approximate value for large drops; or, for a body moving horizontally, the approximate stress with its kinetic energy in place of weight × height; checked against your allowable stress.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Member struck | choice | The member that takes the shock and how it is supported; springs are close-coiled helical springs. |
| Shock | choice | Whether a weight falls onto the member, or a body moves horizontally into it so only its kinetic energy acts. |
| Beam | ||
| Span (cantilever length) | mm | Distance between supports, or the cantilever length to the point struck. |
| Second moment of area | mm⁴ | Second moment of area of the beam section about its bending axis. |
| Distance from neutral axis to extreme fibre | mm | Distance from the neutral axis to the outermost fibre, for example half the depth of a symmetrical section. |
| Modulus of elasticity | MPa | Elastic modulus of the beam material, from the material data. |
| Spring | ||
| Mean coil diameter | mm | Mean diameter of the spring coils (outside diameter less one wire diameter). |
| Wire diameter (side of square wire) | mm | Wire diameter of a round-wire spring, or the side of a square-wire spring. |
| Active coils | Number of active coils that deflect under load. | |
| Shear modulus | MPa | Shear modulus of the spring material, from the material data. |
| Load | ||
| Mass of the falling or moving body | kg | Mass of the body that falls or moves into the member. |
| Drop height before striking | mm | Height the weight falls before it touches the member. |
| Speed of the moving body | m/s | Horizontal speed of the moving body at impact (used for the moving-body shock only). |
| Allowable stress | MPa | Largest stress you allow in the member under the shock, from your material data and design code. |
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: Member struck
- What it is
- The member that takes the shock and how it is supported or wound.
- Units and format
- Choose one of 5 options from the list: Beam, simply supported, struck at the centre; Beam, cantilever, struck at the free end; Beam, fixed at both ends, struck at the centre; Helical spring, round wire; Helical spring, square wire.
- Example
- The form opens with “Beam, simply supported, struck at the centre” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Changes the static stress and stiffness, and so the peak stress.
- Get it right
- Pick the beam case nearest your supports, or a helical spring of round or square wire.
What this means: Shock
- What it is
- Whether a weight falls onto the member or a body moves horizontally into it.
- Units and format
- Choose one of 2 options from the list: Weight dropped through a height; Body moving horizontally into the member.
- Example
- The form opens with “Weight dropped through a height” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- For a moving body only its kinetic energy acts, so the approximate formula is used.
- Get it right
- Choose the moving body for carriages, trolleys or slides hitting a stop.
Beam
What this means: Span (cantilever length)
- What it is
- Distance between the beam supports, or the length of a cantilever to the point struck.
- 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 1000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer beam is more flexible, which lowers the shock stress.
- Get it right
- Use centre-to-centre of the supports.
What this means: Second moment of area
- What it is
- Second moment of area of the beam section about the bending axis.
- 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 8330000 mm⁴ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A stiffer section raises the static part of the peak but lowers the stress overall.
- Get it right
- For a solid rectangle it is b h³ ÷ 12; use the section tables for rolled shapes.
What this means: Distance from neutral axis to extreme fibre
- What it is
- Distance from the neutral axis to the outermost fibre of the beam.
- 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.
- Effect on the result
- The stress is directly proportional to this distance.
- Get it right
- Half the depth for a symmetrical section.
What this means: Modulus of elasticity
- What it is
- Elastic modulus of the beam material.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 100 MPa to 1000000 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
- A stiffer material takes the energy over a shorter deflection, so the stress is higher.
- Get it right
- Take it from your material data; about 200 000 MPa for steel.
Spring
What this means: Mean coil diameter
- What it is
- Mean coil diameter of the spring: outside diameter less one wire diameter.
- 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.
- Effect on the result
- A larger coil lowers the spring rate and spreads the energy over more deflection.
- Get it right
- Measure the outside diameter and subtract the wire size.
What this means: Wire diameter (side of square wire)
- What it is
- Wire diameter of a round-wire spring, or the side of a square-wire spring.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Thicker wire stiffens the spring sharply and raises the shock stress.
- Get it right
- Measure the wire with a micrometer.
What this means: Active coils
- What it is
- Number of active coils that deflect under load.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 1000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More active coils lower the rate and the shock stress.
- Get it right
- Total coils less the closed and ground end coils (usually two).
What this means: Shear modulus
- What it is
- Shear modulus of the spring material.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 100 MPa to 1000000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 79300 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher modulus raises the shock stress for the same energy.
- Get it right
- Take it from your material data; about 79 000 MPa for spring steel.
Load
What this means: Mass of the falling or moving body
- What it is
- Mass of the body that falls or moves into the member.
- 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
- More mass means more energy and a higher peak stress.
- Get it right
- Include everything that moves with the body at impact.
What this means: Drop height before striking
- What it is
- Height the weight falls before it touches the member.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 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
- The peak stress rises roughly with the square root of the height.
- Get it right
- Measure from the bottom of the weight to the top of the member.
What this means: Speed of the moving body
- What it is
- Horizontal speed of the moving body at the moment of impact.
- Units and format
- Enter a number in m/s: metres per second. The form accepts 0 m/s to 1000 m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The energy and the stress rise with the speed; the stress in proportion to it.
- Get it right
- Use the highest speed the drive or a runaway can reach.
What this means: Allowable stress
- What it is
- Largest stress you allow in the member under the shock.
- 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 300 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line.
- Get it right
- Base it on yield strength with your design code's factor.
Method and formulas
- Weight Q = M g with g = 9.81 m/s²; energy Q h for a drop, ½ M v² for a moving body (Qh = 1000 × ½ M v² N·mm).
- Beams: static stress p_s = Q a L ÷ (k I) and static deflection y = 2 Q L³ ÷ (c E I), with k = 4, 1, 8 and c = 96, 6, 384 for simply supported, cantilever and fixed-ended beams; peak p = p_s(1 + √(1 + c h E I ÷ (Q L³))) = p_s(1 + √(1 + 2h ÷ y)); approximately p = a √(6 Q h E ÷ (L I)).
- Round-wire springs: f_s = 8QD ÷ (π d³); f = f_s(1 + √(1 + G h d⁴ ÷ (4 Q D³ n))); approximately f = 1.27 √(Q h G ÷ (D d² n)).
- Square-wire springs: f_s = 9QD ÷ (4d³); f = f_s(1 + √(1 + G h d⁴ ÷ (0.9π Q D³ n))); approximately f = 1.34 √(Q h G ÷ (D d² n)).
- For a body moving horizontally the approximate formula is used with ½ M v² in place of Q h.
- Example: 20 kg dropped 50 mm onto the beam gives a peak stress of 59.734 MPa, 202.89 times the static stress, against 300 MPa allowed.
Limitations
- The member is assumed to take all the shock energy elastically, with no loss at impact and no mass of its own; the result is an upper bound, as the handbook notes.
- Spring stresses are the uncorrected torsional stresses the handbook gives; the curvature (Wahl) factor raises the stress at the coil inside.
- Local stresses at the point of impact and yielding are not covered.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a beam, stop or buffer spring for a dropped load
- Estimate the stress when a moving carriage hits a stop
- Compare round and square wire springs for shock
Who it is for
- Machine designers
- Structural and mechanical engineers
- Safety reviewers
What you get
- Shock energy
- Static stress and deflection under the weight
- Peak stress by the full formula and the approximation
- Impact factor (peak ÷ static stress)
- Peak stress against the allowable
Interpreting the result
- A load dropped from zero height still doubles the static stress: the impact factor is never below 2.
- The approximate formula shows the stress rises with the square root of the energy, so halving the drop height lowers the stress by about 30 %.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 278–280. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Useful alongside · KEVOS® original book
Load paths: what a weld must carry
In Designing Welded Joints by the Numbers
What it covers: Trace how force passes from one part to another through a welded joint, name the joint types and weld types, and see why a weld's strength depends on its fused throat, not its appearance.
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