A live moment-balance calculator for the tower cranes that shape every modern city skyline. Slide jib length, counterweight, load radius and wind speed and watch the overturning moment, restoring moment and stability factor update in real time, so you can design a crane that does not tip over.
Parameters
Crane type
Hammerhead is the mainstream default; luffing and self-erecting for reference
Jib length
m
Counter-jib length
m
Counterweight
ton
Concrete blocks loaded near the tip of the counter-jib
Load radius
m
Horizontal distance from slewing centre to the hoisted load (trolley position)
Load mass
ton
Jib mass per metre
kg/m
Linear self-weight of the lattice jib. Real machines: 200–500 kg/m
Wind speed
m/s
Stop hoisting above 14 m/s; release the slew brake above 20 m/s
Results
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Jib self-weight moment (ton·m)
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Load moment (ton·m)
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Restoring moment (ton·m)
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Stability factor
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Max lifting capacity (ton)
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Wind load (kN)
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Tower crane side view — moment balance animation
Side view of the mast, jib, counter-jib, hoisted load and slewing centre. The red arrow shows the overturning moment, the blue arrow the restoring moment.
Lifting capacity vs radius (load chart)
Counterweight sensitivity — stability factor SF
Theory & Key Formulas
$$M_{net} = M_{load} \cdot R - M_{cw} \cdot R_{cw},\quad SF = \frac{M_{restore}}{M_{overturn}} \geq 1.0$$
M_load = load, R = radius, M_cw = counterweight, R_cw = counter-jib radius. SF is the ratio of restoring to overturning moment about the slewing centre.
With ρ = 1.225 kg/m³ and C_d = 1.4, the horizontal wind force scales with V² and acts on the projected jib area.
Tower Crane Counter-Jib Balance — Overturning Moment
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Those huge cranes you see sticking out above urban building sites — long jib in front, short arm with a chunk of concrete at the back — how exactly do they stay up?
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Great thing to ask. That is a tower crane, specifically the horizontal-jib "hammerhead" type that dominates today's skylines. Mechanically it is a seesaw: a "jib" reaches forward with the load and a "counter-jib" carrying concrete blocks reaches back, and you balance their moments about the slewing centre. The classic rule is load × radius ≈ counterweight × counter-jib length, with a stability factor SF ≥ 1.3 as design margin. Liebherr 280EC-H and China's ZOOMLION D5200 (25 ton at 80 m, one of the largest in the world) are textbook examples.
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A seesaw — that clicks. So if I extend the jib and lift the load farther out, I need a heavier block at the back, otherwise the crane tips forward?
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Exactly. Try sliding the load radius R up to 80 m on the left. The load moment M_load = m·R jumps and the stability factor drops fast. Every real crane has a load chart that ties the maximum lift to the radius. The Kroll K-10000 used on Burj Khalifa (UAE, 828 m) lifts 22 ton at 100 m radius; the Liebherr 280EC-H lifts 12 ton at 12 m but only 2.8 ton at 70 m, and the chart on the right reproduces that hyperbolic (1/R) decay.
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There is also a wind-speed slider. People say a crane in a typhoon ends up spinning around like a weather vane — is that safe, or actually dangerous?
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It is the safe state. Above a 10-minute average wind of 14 m/s (Japanese Crane Safety Rule §74-3) lifting stops; above 20 m/s the slew brake is released and the jib enters "weather-vaning" mode. If the jib stayed fixed against the wind, F_wind = ½·ρ·V²·A would create a huge horizontal moment on the mast; freed to slew, the jib swings downwind and presents the minimum frontal area. The 2008 New York 51st Street collapse (7 deaths) and the 2015 Mecca Masjid al-Haram disaster (111 deaths) were both linked to wind-load management and foundation strength failures.
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The model selector lists "Luffer" and "Self-erecting". What is the practical difference — isn't hammerhead enough for everything?
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Each shines in a different niche. A "Luffer" can raise and lower its jib like a derrick, perfect for dense downtown sites with very little clearance to neighbouring buildings — Shimizu and Liebherr LR types are common. A "Self-erecting" crane (Potain HD/Igo, Spierings) arrives on a trailer and erects in a few hours; in Japan it is rented for a single day on housing-development sites. For super-tall builds like Shanghai Tower (632 m) or Tokyo Skytree (634 m), several hammerheads run in parallel and climb upward with the structure.
Frequently Asked Questions
It is the moment ratio SF = M_restore / M_overturn about the slewing centre. M_overturn is the sum of the load moment (load mass × radius) and the jib self-weight moment (jib mass × jib length / 2); M_restore is the sum of the counterweight moment (CW mass × counter-jib length) and the counter-jib self-weight moment. ASME B30.3 and the Japanese Crane Safety Rules require SF ≥ 1.3 during operation as a baseline, and SF ≥ 1.1 as a minimum for storm stand-by. This tool flags SF < 1.0 as overturning and SF = 1.0–1.3 as a warning.
For a hammerhead crane, lifting operations stop at a 10-minute average wind speed of 14 m/s (Japanese Crane Safety Rule §74-3); above 20 m/s the slew brake is released so the jib goes weather-vaning. Luffing cranes are tilted up to 70° or more before stand-by. This tool flags V > 15 m/s as a warning and estimates F_wind ≈ 0.5·ρ·V²·A·C_d as the horizontal force on the jib projected area. Real designs use EN 13001-2 / JIS B 8821 with a gust factor (≈1.4) and machine-specific C_d (1.2–1.8).
Load moment M_load = m·R grows linearly with radius R, while the counterweight moment M_cw = M_cw·R_cw stays constant. Maximum lift becomes m_max = (M_cw + M_cj − M_jib) / R, so doubling R roughly halves the capacity. The Liebherr 280EC-H quotes 12 ton at 12 m and 2.8 ton at 70 m in its load chart, and this tool's max_load_at_radius reproduces that hyperbolic decay.
Solve for CW with M_cw = (M_load + M_jib − M_counterJib) / R_cw. For a 50 m jib lifting 3 t at 40 m radius, M_load + M_jib ≈ 495 ton·m. With R_cw = 14 m, the required CW is about 35 ton; in practice 40–45 ton is loaded to keep SF ≥ 1.3. When this tool's "max lifting capacity" goes negative, the jib's own weight already overturns the crane even before any load is hung.
Real-World Applications
Super-tall building construction: Burj Khalifa (UAE, 828 m, completed 2010) was built with five Kroll K-10000 cranes (22 ton at 100 m radius, one of the largest in the world). Shanghai Tower (632 m, 2015) used China's ZOOMLION D5200 (25 ton at 80 m) alongside Manitowoc machines. Tokyo Skytree (634 m, 2012) was assembled with three hammerheads climbing upward with the structure. Setting this tool to ZOOMLION D5200-class numbers (counterweight ≥ 40 t, jib 80 m) reproduces SF ≥ 1.3 for 10-ton lifts at 60 m radius.
Urban redevelopment in tight sites: Liebherr LR and Comansa LCL luffing cranes can raise the jib like a derrick, so they dominate sites where the clearance to neighbouring buildings is under 5 m — Tokyo Station front redevelopment, Hong Kong ICC (484 m), and similar projects. Tilting the jib to 70° cuts the swing radius to about a third, preventing trespass over adjacent property. Select "Luffer" in the simulator and shorten the effective jib length to see this effect.
Housing and small construction sites: Potain Igo and Spierings (truck-mounted, Netherlands) self-erecting cranes have a 20–35 m jib and 5–10 t counterweight, arrive on a single trailer and erect in 2–4 hours. In Japan they are rented for a single day on housing-development sites to lift roof material and gutters. This tool's 20-m jib, 5–10 t CW region covers that class.
Accidents and risk management: The 2008 New York 51st Street collapse (turnbuckle failure, 7 dead), the 2015 Mecca Masjid al-Haram collapse (luffing jib failure in strong wind, 111 dead), and the 2019 Seattle Google-campus accident (loss of structural support during dismantling) all came down to mismanagement of stability factor, wind load or foundation strength. The stability factor and F_wind outputs of this tool show how early-design calculations can rule out these scenarios.
Common Misconceptions and Pitfalls
The biggest pitfall is treating the jib self-weight as uniformly distributed. The formula M_jib = m_jib·L/2 used here assumes the centre of gravity sits at mid-length. In real lattice jibs the boom-head end carries sheaves, hoist ropes, trolley rails and electrics, shifting the CG 5-15% toward the tip. Liebherr and Potain design guides use x_g/L = 0.55-0.58, so the real M_jib is a few percent higher than the tool's value. To stay on the safe side, recheck the stability factor with M_jib multiplied by 1.10-1.15.
Next, relying on a static balance check alone. A real tower crane slews, hoists and trolleys constantly; load swing (pendulation) at slew start/stop can momentarily amplify the moment by 1.3-1.5×. The Japanese Crane Safety Rules and ASME B30.3 set this dynamic amplification factor (DAF) to 1.25 — designers add 25% to the static value. The tool's SF ≥ 1.3 verdict already absorbs that DAF, so the 1.0-1.3 warning band means "could overturn under dynamic loads".
Finally, "more counterweight is always safer" is not true. Loading too much CW makes the restoring moment dominate when no load is hung, and the crane can fall backwards (back-fall). Real machines have a minimum-load rule, and some load charts even state "always carry at least 0.5 t to keep the balance". Try 0.5 t load with 50 t counterweight in this tool: the SF inflates several-fold and the balance leans dangerously backward. Foundations must be designed symmetric about the slewing centre to resist both directions.
How to Use
Enter jib length (typically 40–60 m for Liebherr LTM series) and counter-jib length (8–15 m).
Set counter-weight mass in tonnes (15–25 t standard) and load radius from tower centerline in metres.
Read real-time moment balance: jib self-weight moment, load moment, restoring moment from counter-weight, stability factor (target ≥1.3), and maximum safe lifting capacity in tonnes.
Worked Example
Liebherr LTM 1300-6.1 configuration: jib length 50 m, counter-jib 12 m, counter-weight 20 tonnes at 2 m from tower. Operator loads 45 tonnes at 28 m radius. Jib self-weight moment ≈ 480 ton·m. Load moment = 45 × 28 = 1,260 ton·m. Restoring moment = 20 × 2 = 40 ton·m (insufficient alone; gravity on jib extends balance arm). Stability factor 1.28 approaches critical threshold. Wind load at 12 m/s adds 18 kN side force; reduce load to 38 tonnes for factor ≥1.30.
Practical Notes
Stability factor below 1.25 triggers load-limiting protocol on modern cranes; redundancy required for 200+ tonne lifts in urban sites.
Counter-weight placement (typically 1.5–3.0 m from mast) is fixed at factory; jib length extension demands ballast repositioning per structural certification.
Wind loading compounds moment imbalance exponentially above 10 m/s; most regional codes impose 15 m/s operational cutoff and automatic load reduction algorithms.