Crane Load Moment
Calculate a crane's load moment, M = W·R, from the load weight W (N) and the operating radius R (m, the horizontal distance from the crane's rotation center to the load). The load moment is the product of the load weight and its distance to the crane's rotation axis, and it GOVERNS the TIPPING stability — the most feared and catastrophic crane failure mode. A crane tips when the load moment (tending to overturn it forward, toward the load) exceeds the STABILIZING moment (the crane's own weight and counterweight, acting backward). The genius — and danger — is in the RADIUS: the SAME load generates a much larger moment when far (boom extended) than near (boom retracted). So a crane's capacity is NOT a single number, but a LOAD CHART that drops drastically as the radius grows — a crane lifting 50 tonnes at 5 m radius may lift only 5 tonnes at 30 m. Exceeding the maximum load moment (the 'load curve') is the main cause of crane tipping, so cranes have load moment indicators (LMI) locking operation near the limit. Computing the load moment and comparing it with the allowable moment for that radius is the fundamental safety check in every crane operation. Enter the load weight and the operating radius.
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Crane load moment
The load moment of a crane is M = W·R, from the load weight W and the operating radius R (the horizontal distance from the center of rotation of the crane to the load). It is the product of the load weight by its distance to the slewing axis, and it is the parameter that governs stability against tipping — the most feared and most catastrophic failure mode in crane work. A crane tips over when the load moment (which tends to pull it forward, towards the load) exceeds the stabilizing moment (the weight of the crane itself plus the counterweight, acting backwards). The brilliance — and the danger — lies in the radius: the same load produces a much larger moment when it sits far out (boom extended) than when it is close in (boom retracted). That is why the capacity of a crane is never a single number, but a load chart that drops sharply as the radius grows — a crane that lifts 50 tonnes at a 5 m radius may lift only 5 tonnes at 30 m. Exceeding the maximum load moment (the 'load curve') is the leading cause of crane tip-overs, which is why cranes carry load moment indicators (LMI) that lock out the operation as the limit is approached. Computing the load moment and checking it against the value allowed at that radius is the fundamental safety verification in every lifting operation. Enter the load weight and the operating radius.
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Calculate a wire rope's safety factor, SF = breaking load ÷ working load, from the minimum breaking load (MBL, N) and the applied working load (N). Wire ropes, used in cranes, elevators, cableways, bridges, lifting and mooring, work with HIGH safety factors — far higher than static structures — for several reasons: the load is rarely static (there are impacts, accelerations, swings), the rope wears and loses strength over use (wires break, corrosion and fatigue occur), and a rupture is catastrophic (load drop, life risk). Codes prescribe minimum safety factors per application: typically 5 for general load lifting, 6-8 for people-carrying ropes (elevators, cableways), 3-4 for static stays and moorings, and specific values per use. The safety factor is the ratio between the load that would break the rope (its rated strength, from the maker) and the load it actually carries in service. Checking that the real safety factor meets the code minimum is the basic safety check of any wire-rope application — and the rope must be DISCARDED when wear reduces its strength enough for the factor to fall below the limit. Enter the breaking load and the working load.
Wire Rope Working Load Limit (WLL)
Calculate a wire rope's allowable working load, WLL = MBL ÷ SF, from the minimum breaking load (MBL, N) and the required safety factor. The working load (WLL — Working Load Limit, or SWL — Safe Working Load) is the MAXIMUM load that can be safely applied to a rope, fitting or lifting equipment — the information STAMPED on slings, shackles, hooks and equipment plates, and what the operator uses to decide whether a given load can be lifted. It is obtained by dividing the breaking load (the real strength that would break the component) by the code safety factor (5 for general lifting, more for special situations). Respecting the WLL is an absolute safety rule in lifting and material-handling: exceeding the working load dangerously approaches the component to rupture, eliminating the safety margin covering dynamic effects, wear and uncertainties. The WLL is not the rope's strength — it is the SAFE fraction of it. Every rigging operation starts by checking that the load to lift is below the WLL of each component in the load line (rope, slings, shackles, hook, eye), since the chain is only as strong as its weakest link. Enter the breaking load and the safety factor.
Metacentric Height (GM)
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Calculate the linear loading density of a blast hole, q = (π/4) × d² × ρ, from the hole diameter d (mm) and the explosive density ρ (g/cm³). The result, in kg of explosive per meter of hole, is how much explosive fits in each meter of charged column — a central parameter of rock blast design. Multiplied by the hole charge height, it gives the charge per hole; combined with the blasted rock volume, it gives the powder factor. Larger diameters and denser explosives raise the linear charge. Enter the hole diameter and the explosive density.
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Calculate the residual clamping force on the members (clamped parts) of a bolted joint under external load, F_m = F_i − (1 − C)·P, from the preload F_i (N), the joint stiffness constant C and the external tensile load P (N). When an external load P tries to separate the parts, it does not go entirely to the bolt — most, (1−C)·P, acts to RELIEVE the compression between the members. The residual force F_m is how much clamping STILL holds the parts together after the external load is applied. This value is crucial for several reasons: while F_m stays POSITIVE (compression), the joint is closed and tight, and the bolt is protected (feels only C·P); if F_m reaches ZERO, the joint SEPARATES (and the bolt takes the whole load). In SEALED joints (gaskets, engine joints, pressurized pipe flanges), the residual member force is what keeps the seal compressed and prevents leaks — so it must stay above a minimum value, even under maximum service load (internal pressure, for example). Computing F_m is essential to ensure the joint stays tight and sealed in operation, and it is the criterion that sets the minimum required preload. Enter the preload, the stiffness constant and the external load.
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