Moment of Force Converter
Convert moment of force units including N·m, lbf·ft, kgf·m, and more. Free online bending moment converter for structural and mechanical engineering calculations.
Understanding Moment of Force
Moment of force measures the bending or turning effect of a force about a point or axis. You express it in newton-meters (N·m). Moment of force equals force multiplied by the perpendicular distance from the point to the line of action.
Moment of force is synonymous with torque in many contexts. In structural engineering, moment typically refers to bending moment in beams. In mechanics, moment and torque are often used interchangeably.
Moment of Force Formulas
M = F × d
Definition: Moment equals force times perpendicular distance (moment arm). Units are N·m or lbf·ft.
M = w × L² / 8
Simply supported beam: Maximum bending moment for uniformly distributed load w over span L.
M = P × L
Cantilever beam: Maximum moment for point load P at end of cantilever length L.
σ = M × y / I
Bending stress: Stress equals moment times distance from neutral axis divided by moment of inertia.
Example: A 500 N force applied 2 m from a pivot produces M = 500 × 2 = 1,000 N·m moment.
Common Moment Conversions
| N·m | lbf·ft | kgf·m | kgf·cm |
|---|---|---|---|
| 0.138 | 0.1 | 0.0141 | 1.41 |
| 1.356 | 1 | 0.138 | 13.8 |
| 1 | 0.738 | 0.102 | 10.2 |
| 9.807 | 7.23 | 1 | 100 |
| 0.0981 | 0.0723 | 0.01 | 1 |
Beam Moment Formulas
| Beam Type | Loading | Max Moment |
|---|---|---|
| Simply Supported | Center Point Load P | PL/4 |
| Simply Supported | Uniform Load w | wL²/8 |
| Cantilever | End Point Load P | PL |
| Cantilever | Uniform Load w | wL²/2 |
| Fixed-Fixed | Center Point Load P | PL/8 |
| Fixed-Fixed | Uniform Load w | wL²/12 |
Practical Applications
Structural Beam Design
Beams resist bending moments from loads. Steel I-beams efficiently resist bending. Concrete beams require reinforcement in tension zone. Moment diagrams show variation along beam length.
Shaft Design
Rotating shafts experience bending moments from gears and pulleys. Combined with torsion, this creates complex stress states. Shaft diameter depends on allowable stress and applied moments.
Lever Systems
Levers multiply force using moment principles. Mechanical advantage equals effort arm divided by load arm. Crowbars, pliers, and seesaws all use moment principles.
Crane and Hoist Design
Crane booms experience large bending moments. Load moment equals weight times radius. Load charts specify capacity at each radius. Overloading causes structural failure.
Frequently Asked Questions
What is the difference between moment and torque?
Moment and torque are mathematically identical. Torque typically refers to twisting about an axis. Moment often refers to bending. Both use same units and formulas.
What is a bending moment diagram?
Bending moment diagram shows moment variation along a beam. Plot moment values at each point. Maximum moment occurs where shear force equals zero. Used for beam design.
How do you calculate moment arm?
Moment arm is perpendicular distance from pivot to force line of action. For angled forces, use d = r × sin(θ) where r is distance to force application point.
What causes beam failure?
Excessive bending moment causes failure. Tension side cracks in concrete. Compression side buckles in thin sections. Shear failure occurs near supports. Proper sizing prevents failure.
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