What calculations should a lift engineer be able to do by hand?

Seven cover most of what gets asked in a meeting: sling tension at an angle, load share between lift points, centre of gravity from component masses, the three plate checks at a pin hole, a weld group under a moment, ground bearing pressure under a mat, and the difference between a spreader's compression and a lifting beam's moment. Every one is classical mechanics, and the value is speed rather than accuracy - a number in ninety seconds changes a decision while the decision is still open.

How do you calculate the stress at a padeye hole by hand?

Three areas and one force. Net section is the plate either side of the hole, so plate width minus hole diameter, times thickness. Bearing is the pin's projected area, so pin diameter times thickness. Shear-out is two planes from the hole to the free edge, so twice the edge distance minus half the hole diameter, times thickness. Divide the leg tension by each area in turn. Each result is a stress and none is an answer until it meets an allowable from a design route.

How do you hand-check a lug weld?

Resolve the sling force along and across the plate, multiply the transverse component by the pin's height above the weld to get a moment, then compute two stresses: the axial force over the weld group's throat area, and the moment over its section modulus. The throat is the fillet leg divided by the square root of two, and the section modulus of two parallel runs is twice the throat times the run length squared over six. On the worked example at only 12 degrees off axis the bending term already exceeds the direct one.

What does a calculation tool add if the hand calculation is exact?

Not accuracy - the hand calculation is exact as far as it goes. What it adds is the design route and its allowables, the checks a quick calculation leaves out, and a record with a provenance for every input. In the worked padeye the engine reproduces every hand-calculated stress as a utilisation and adds two checks the pencil did not include. The honest split is that the pencil makes decisions in meetings and the record hands work to somebody who has to accept it.

What is the limit of a hand calculation in rigging?

Each of the seven has a specific boundary. Sling tension assumes the share and the built angle are right. Load share is exact for two and three lift points and has no unique answer for four. A centre of gravity from parts is only as good as its masses and produces a point where an envelope is needed. The plate and weld checks produce stresses that need a route-specific allowable. Ground pressure needs a defensible spread angle and a provenance for the allowable. Beam actions ignore buckling and the pin eccentricity on a spreader.

Rigging calculations: seven to do on paper

The short answer

Seven calculations cover most of what a lift engineer is asked in a meeting, and every one of them is public-domain mechanics you can do on the back of a drawing.
They are worth being able to do not because software is unreliable, but because a number you can produce in ninety seconds is the one that changes a decision while the decision is still open.
Each of the seven has a boundary. Knowing the boundary is the part that separates a useful hand calculation from a dangerous one.
A hand calculation tells you the size of the answer. A traceable calculation tells a reviewer where every input came from. Both are needed and they are not the same document.
The worked padeye below is checked twice, once by hand and once by the engine, and the point of showing both is what the second one adds to the first.

Sling tension at an angle

Share, then one over the sine. The single most useful number in rigging and the one people most often get by dividing the total by the number of legs.

Sling tension at an angle

T = \frac{V}{sin θ}

$V$: is the vertical share carried by this leg
$θ$: is that leg's own angle from the horizontal

A 16 t load on two legs at 55 degrees:

V T H = \frac{157.0}{2} = 78.5 kN = \frac{78.5}{sin 5 5 ^{\circ}} = 95.8 kN = \frac{78.5}{tan 5 5 ^{\circ}} = 55.0 kN vertical share per leg leg tension inward pull at each lift point

The three numbers this calculation produces, in one picture. The inward pull is 70 percent of the vertical share at this angle and exceeds it below 45 degrees.

The boundary. It assumes the share is right, which on anything but a symmetric two-leg pick it is not. It also assumes the angle is the built one rather than the drawn one. Both of those are separate calculations.

Centre of gravity from parts

The mass-weighted average. It is the input calculation two depends on, and it is the one most often taken off a drawing without a tolerance.

Centre of gravity from parts

\overset{x}{ˉ} = \frac{\sum m _{i} x _{i}}{\sum m _{i}}

$m_{i}$: is the mass of part i
$x_{i}$: is that part's own centroid, measured from a stated datum

A 16.3 t machine in four parts:

Part	Mass	x	m · x
Base frame	3,000 kg	2.50 m	7500
Drum	8,500 kg	1.40 m	11900
Gearbox	2,400 kg	3.80 m	9120
Guarding and misc	2,400 kg	3.00 m	7200
Total	16,300 kg	2.191 m	35720

The boundary. It is only as good as the masses, and it produces a point where what you need is an envelope. The useful follow-up is the sensitivity: change the heaviest part by a realistic error and see how far the answer moves.

The three plate checks at a pin hole

Net section, bearing and shear-out. Three areas and one force. Nothing here is proprietary and all three can be drawn on the plate with a pencil.

Take the 95.8 kN from calculation one into a padeye: 30 mm plate, 240 mm wide, 58 mm hole on a 54 mm pin, 85 mm from the hole centre to the top edge.

Net section. The plate either side of the hole, in tension.

A_{net} σ_{net} = (240 - 58) \times 30 = 5460 mm^{2} = \frac{95806}{5460} = 17.5 MPa

Bearing. The pin's projected area on the plate.

A_{b} σ_{b} = 54 \times 30 = 1620 mm^{2} = \frac{95806}{1620} = 59.1 MPa

Shear-out. Two planes from the hole to the free edge.

A_{sh} τ_{sh} = 2 (85 - \frac{58}{2}) \times 30 = 3360 mm^{2} = \frac{95806}{3360} = 28.5 MPa

The boundary. Every one of these is a stress, and a stress is not an answer until it is compared with an allowable that you can defend. That allowable comes from a design route, and the route is the part a hand calculation cannot supply.

A weld group under a moment

Throat area and section modulus, then two stress terms. It is the one calculation on this list people routinely do wrong, because they do only the first term.

The same padeye, welded all round with a 12 mm fillet 220 mm long each side, pin 180 mm above the weld, sling 12 degrees off the plate axis.

Resolve the force, and take the moment.

N V M = 95.8 cos 1 2^{\circ} = 93.7 kN = 95.8 sin 1 2^{\circ} = 19.9 kN = 19.9 \times 180 = 3.59 kN m

The weld group's properties.

a_{th} A_{w} S_{w} = \frac{12}{2} = 8.49 mm = 2 \times 220 \times 8.49 = 3734 mm^{2} = \frac{2 \times 8.49 \times 22 0 ^{2}}{6} = 136896 mm^{3}

The two terms.

σ_{direct} σ_{bending} = \frac{N}{A _{w}} = 25.1 MPa = \frac{M}{S _{w}} = 26.2 MPa

At only 12 degrees off axis the bending term is already the larger of the two. That is the single most useful thing on this page.

The boundary. The sum of those two acts on the weld's leg and has to be resolved onto its throat, then combined with the in-plane shear, and then compared with a route-specific allowable. The hand calculation gets you the size of the answer; the route gets you the acceptance.

Ground bearing pressure under a mat

Force over area, and the whole difficulty is which area. A mat's plan area is an upper bound it does not reach.

An outrigger at 520.0 kN on a 0.6 m square float, on a 2.4 m mat 0.4 m thick, with a 30 degree spread declared.

q_{float} s b_{eff} q_{ground} = \frac{520.0}{0.36} = 1444 kPa = 0.4 tan 3 0^{\circ} = 0.231 m = 0.6 + 2 \times 0.231 = 1.062 m = \frac{520.0}{1.13} = 461 kPa under the float alone spread each side effective width pressure on the ground

The credited area is 1.13 m², against 5.76 m² of mat plan area.

That float pressure is several times any soil's capacity, which is why mats exist.

The boundary. The spread angle is a claim about the mat's stiffness that you have to defend, the mat has its own bending and punching checks, and the allowable on the other side of the comparison needs a provenance. Three separate things a single division does not contain.

Beam actions in a spreader and a lifting beam

One is compression, the other is bending, and the arithmetic to tell them apart takes twenty seconds.

A spreader carries the inward pull of the slings as axial compression. From calculation one, that is 55.0 kN on a 5.0 m beam.

A lifting beam carries the same load in bending. With the load at midspan of a simply supported beam:

M = \frac{W L}{4} = \frac{157.0 \times 5.0}{4} = 196.2 kN m

Those two numbers are what decides which device to hire. A section that carries 55.0 kN of compression over 5.0 m is a modest tube; a section that carries 196.2 kN·m of moment over the same span is a substantially heavier beam.

The boundary. A spreader is not a pure strut - the sling pin sits above the beam axis, which hands it a real moment - and its compression capacity is a buckling problem that needs an effective length and a section. Neither of those is a hand calculation.

What a tool adds to the pencil

Not accuracy. The hand calculation above is exact. What it adds is the route, the allowables, the checks you did not think of, and a record somebody else can audit.

Lifting Lug Calculator · computed at page render

The same padeye, checked by the engine

Identical geometry, identical weld, identical load, so the hand calculation and this table are two views of one object.

Design loadthe leg tension from calculation one	95.8kN
Net-section tensionhand calculation gave 17.5 MPa	8.2%
Double-plane shear-outhand calculation gave 28.5 MPa	23.2%
Pin bearing on the lughand calculation gave 59.1 MPa	18.5%
Pin double shearnot in the hand calculation above	9.5%
Fillet weld throat resultantthe two terms resolved onto the throat and combined	19.8%
Fillet weld von Misesa second weld criterion, not in the hand calculation	16.2%

Governing check: Double-plane shear-out (mechanics)23.2% utilisationPass

Every stress the hand calculation produced is here, turned into a utilisation against a declared allowable, alongside two checks the hand calculation did not include. That is the honest split: the pencil gives you the size of the answer in a meeting, and the record gives a reviewer somewhere to start.

Open this example in the calculator

The division of labour that works:

Use the pencil to make decisions. In a meeting, on a site visit, when somebody asks whether a bigger shackle will fit. A number in ninety seconds beats a better number tomorrow, because tomorrow the decision is made.

Use the record to hand work over. When somebody else has to accept, check or reuse the calculation, what matters is that every input has a provenance and every check has a basis. That is a different artefact and it takes longer for good reasons.

Seven things to be able to do without opening anything

01Sling tension at an angleShare divided by the sine of that leg's angle from horizontal, per leg.
02Load share between lift pointsMoments about one point. Exact for two and three, and it has no unique answer for four.
03Centre of gravity from partsMass-weighted average per axis, with a sensitivity for the heaviest part.
04The three plate checks at a pin holeNet section, bearing and shear-out, as three areas and one force.
05A weld group under a momentThroat area and section modulus, then the direct and bending terms separately.
06Ground bearing pressure under a matForce over the credited area, not over the plan area.
07Spreader compression against lifting beam momentThe inward pull, against W L over 4. It decides which device to hire.

Common questions

What calculations should a lift engineer be able to do by hand?: Seven cover most of what gets asked in a meeting: sling tension at an angle, load share between lift points, centre of gravity from component masses, the three plate checks at a pin hole, a weld group under a moment, ground bearing pressure under a mat, and the difference between a spreader's compression and a lifting beam's moment. Every one is classical mechanics, and the value is speed rather than accuracy - a number in ninety seconds changes a decision while the decision is still open.
How do you calculate the stress at a padeye hole by hand?: Three areas and one force. Net section is the plate either side of the hole, so plate width minus hole diameter, times thickness. Bearing is the pin's projected area, so pin diameter times thickness. Shear-out is two planes from the hole to the free edge, so twice the edge distance minus half the hole diameter, times thickness. Divide the leg tension by each area in turn. Each result is a stress and none is an answer until it meets an allowable from a design route.
How do you hand-check a lug weld?: Resolve the sling force along and across the plate, multiply the transverse component by the pin's height above the weld to get a moment, then compute two stresses: the axial force over the weld group's throat area, and the moment over its section modulus. The throat is the fillet leg divided by the square root of two, and the section modulus of two parallel runs is twice the throat times the run length squared over six. On the worked example at only 12 degrees off axis the bending term already exceeds the direct one.
What does a calculation tool add if the hand calculation is exact?: Not accuracy - the hand calculation is exact as far as it goes. What it adds is the design route and its allowables, the checks a quick calculation leaves out, and a record with a provenance for every input. In the worked padeye the engine reproduces every hand-calculated stress as a utilisation and adds two checks the pencil did not include. The honest split is that the pencil makes decisions in meetings and the record hands work to somebody who has to accept it.
What is the limit of a hand calculation in rigging?: Each of the seven has a specific boundary. Sling tension assumes the share and the built angle are right. Load share is exact for two and three lift points and has no unique answer for four. A centre of gravity from parts is only as good as its masses and produces a point where an envelope is needed. The plate and weld checks produce stresses that need a route-specific allowable. Ground pressure needs a defensible spread angle and a provenance for the allowable. Beam actions ignore buckling and the pin eccentricity on a spreader.

Sources

Every document below is linked at its publisher or regulator. Xarpis reproduces no standard text; where a clause is named, the identifier is given so you can find it in your own copy.

EN EurocodesEurocodes: Building the future
European Commission, Joint Research Centre · free portal
The Commission's own Eurocodes portal: the structure of EN 1990 to EN 1999, the database of Nationally Determined Parameters, and the second-generation timetable. The standards themselves are sold by the national bodies, but the NDP database is free and is what decides which partial factors apply in your country.
ASME BTH-1Design of Below-the-Hook Lifting Devices
ASME · paid document
Structural, mechanical and electrical design criteria for below-the-hook lifting devices, used alongside ASME B30.20 which carries the safety requirements. The current edition is BTH-1-2023; Xarpis implements the 2020 edition and says so on every result.
ANSI/AISC 360Specification for Structural Steel Buildings
American Institute of Steel Construction · free to read
The US steel design specification, in both LRFD and ASD. AISC publishes it for free download, which makes it one of the few structural standards a reader can check the same afternoon they read about it.
ASME B30.9Slings
ASME · paid document
The US volume covering alloy steel chain, wire rope, metal mesh, synthetic rope, synthetic webbing and synthetic round slings: rated loads, marking, inspection, and the removal criteria that decide when a sling leaves service. Where published sling rated loads and angle reductions come from.

Run the check properly

Reading about a calculation is not the same as being able to hand one over. These tools produce the traceable record.

Spreader Beam Design Calculator Crane Ground Bearing Pressure & Outrigger Pad Calculator Lifting Trunnion Design Calculator

Something here wrong, or thinner than it should be? Tell us which paragraph and it gets rewritten. Articles carry the date they were last revised for exactly this reason.

Sling tension at an angle

Load share between two lift points

Centre of gravity from parts

The three plate checks at a pin hole

A weld group under a moment

Ground bearing pressure under a mat

Beam actions in a spreader and a lifting beam

What a tool adds to the pencil

Common questions

Sources

Run the check properly