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Crane runways calculation

What are crane runways ?

Different types of cranes

top-mounted crane bridge

underslung crane bridge

monorail hoist block

The main difference between the configurations of these hoisting devices is the working load limit (WLL); see also «lifting point».
From commercially catalogues of overhead travelling crane suppliers, it is generally found that :

for heavy loads, the top-mounted crane bridges have a capacity up to 1200 kN (120T),
for middle range loads, the underslung crane bridges have a capacity up to 125 kN (12.5T).

The crane bridge can be manufactured in hot rolled section or in box section.

Some of the suppliers of overhead travelling crane products and accessories:
ABUS, FAYAT ADC, GH cranes & components, HADEF, KONECRANES, OMIS, SMAK, VERLINDE, ...
Your company is not is the list ? Contact us to add it.

Different types of ways

commercially available profiles

reinforced with angles
for top-mounted crane only !

welded reconstructed sections

The construction of crane runways can be achieved by attachment to the main frames of the buiding or by mounting on independent columns.

For top-mounted crane, they are made of two longitudinal beams (I-shape or box-shape) on which are fixed the rails where the wheels of the crane circulate. In this case, the runways are controlled under torsion effect due to the eccentricity of the vertical and horizontal loads. Some reinforcement can be added to the top flange to prevent excessive torsion or deflection.
For underslung crane, they are also made of two longitudinal beams but the wheels circulate directly on the bottom flange of the beams. Here, additional checking like local bending are required for the bottom flange.
For monorail hoist block, the principle is the same as underslung crane but with only one longitudinal beam and no lateral load.

How to calculate crane runways ?

Step 1 - Loadings calculation from EN 1991-3

Extract of the standard §2.2.1 Classifications of actions - General

(l)P Actions induced by cranes shall be classified as variable and accidental actions which are represented by various models as described in 2.2.2 and 2.2.3.

Extract of the standard §2.2.2 Classifications of actions - Variable actions

(1) For normal service conditions, variable crane actions result from variation in time and location. They include gravity loads including hoist loads, inertial forces caused by acceleration/deceleration and by skewing and other dynamic effects.

(2) The variable crane actions should be separated into:

variable vertical crane actions caused by the self-weight of the crane and the hoist load;
variable horizontal crane actions caused by acceleration or deceleration or by skewing or other dynamic effects.

(3) The various representative values of variable crane actions are characteristic values composed of a static and a dynamic component.

(4) Dynamic components induced by vibration due to inertial and damping forces are in general accounted by dynamic factors φ to be applied to the static action values. (2.1)
where:

F_φ,k is the characteristic value of a crane action;
φ_i is the dynamic factor, see Table 2.1;
F_k is the characteristic static component of a crane action.

(5) The various dynamic factors and their application are listed in Table 2.1.

(6) The simultaneity of the crane load components may be taken into account by considering groups of loads as identified in Table 2.2. Each of these groups of loads should be considered as defining one characteristic crane action for the combination with non-crane loads.
NOTE: The grouping provides that only one horizontal crane action is considered at a time.

Table 2.1 Dynamic factors φ_i
Dynamic factors	Effects to be considered	To be applied to
φ₁	Excitation of the crane structure due to lifting the hoist load off the ground	self-weight of the crane
φ₂	Dynamic effects of transferring the hoist load from the ground to the crane	hoist load
φ₃	Dynamic effects of sudden release of the payload if for example grabs or magnets are used	hoist load
φ₄	Dynamic effects induced when the crane is travelling on rail tracks or runways	self-weight of the crane and hoist load
φ₅	Dynamic effects caused by drive forces	drive forces
φ₆	Dynamic effects of a test load moved by the drives in the way the crane is used	test load
φ₇	Dynamic elastic effects of impact on buffers	buffer loads

Table 2.2 - Groups of loads and dynamic factors to be considered as one characteristic crane action
		Symbol	Section	Groups of loads
				Ultimate Limit State							Test load	Accidental
				1	2	3	4	5	6	7	8	9	10
1	Self-weight of crane	Q_c	2.6	φ₁	φ₁	1	φ₄	φ₄	φ₄	1	φ₁	1	1
2	Hoist load	Q_h	2.6	φ₂	φ₃	-	φ₄	φ₄	φ₄	η⁽¹⁾	-	1	1
3	Acceleration of crane bridge	H_L, H_T	2.7	φ₅	φ₅	φ₅	φ₅	-	-	-	φ₅	-	-
4	Skewing of crane bridge	H_S	2.7	-	-	-	-	1	-	-	-	-	-
5	Acceleration or braking of crab or hoist block	H_T3	2.7	-	-	-	-	-	1	-	-	-	-
6	In-service wind	F_w	Annex A	1	1	1	1	1	-	-	1	-	-
7	Test load	Q_T	2.10	-	-	-	-	-	-	-	φ₆	-	-
8	Buffer force	H_B	2.11	-	-	-	-	-	-	-	-	φ₇	-
9	Tilting force	H_TA	2.11	-	-	-	-	-	-	-	-	-	1
¹ η is the proportion of the hoist load that remains when the payload is removed, but is not included in the self-weight of the crane.

Step 2 - Iterative mechanical analysis

Each of the crane bridge longitudinal positions (along the runway) and transversal positions (staggered or skewed wheels with respect to the rail axis) must be analyzed to detect maximum forces and deformations.

We have developed a specific mechanical solver to do exactly this job.

Step 3 - Serviceability Limit States checkings from EN 1993-6

Four main criteria should be checked, the limiting values of :

vertical deflection of the runway beam : generally L/600
horizontal deflection of the flange supporting the crane : generally L/600
web breathing : generally b/t_w < 120
vibration of the bottom flange : generally L_f / i_f,z ⩽ 250

Some other criteria may have to be checked.

Step 4 - Ultimate Limit States checkings from EN 1993-6

For a top-mounted crane bridge :

Torsion caused by loads eccentricity
Stresses - Von Mises criteria
Transverse buckling of the flanges
Local buckling :
- Local buckling of the flanges
- Local buckling of the web under shear
- Local buckling of the web under point load
- Interactions between local buckling type

Extracts of results given by the software

See the features of Crane Runways
Available in English/French, otherwise «Google Translate»!

B2 - Way geometry and section parameters
B21 - Runway element

B22 - Cross section

Minimum steel grade of the elements : S275 (f_y = 275 MPa, E = 210000 MPa)
Runway section : IPE360
Rail section : 50x30 (the rail is welded on the runway and the wear of the rail of 25% is taken into account in the calculations of the characteristics.)

	Mechanical characteristics : Area : A=91.6 cm² Shear areas : on z-z : : A_sz=42.7 cm² top flange on y-y : A_sy,top=25.6 cm² bottom flange on y-y : A_sy,bot=21.6 cm² Second moments of area : about y-y : I_y=21261.3 cm⁴ (with : : z_G = 21.7cm) top flange about z-z : I_z=1529.4 cm⁴ bottom flange about z-z : I_z=521.1 cm⁴
	Mechanical characteristics : Area : A=84.0 cm² Shear areas : on z-z : : A_sz=35.1 cm² top flange on y-y : A_sy,top=21.6 cm² bottom flange on y-y : A_sy,bot=21.6 cm² Second moments of area : about y-y : I_y=19834.0 cm⁴ (with : : z_G = 20.6cm) top flange about z-z : I_z=544.5 cm⁴ bottom flange about z-z : I_z=521.1 cm⁴

F1 - Ultimate Limit States F11 - Stresses and Von Mises criteria §6.2

EN1993-1-1 (6.1)

	top flange				web top		bottom flange				flanges middle
Span	right above	left above	right below	left below	right	left	right above	left above	right below	left below	above	below
1	163.4MPa	110.3MPa	151.9MPa	101.2MPa	50.4MPa	91.9MPa	101.9MPa	87.4MPa	105.7MPa	91.4MPa	48.0MPa	73.0MPa
2	169.8MPa	120.6MPa	167.8MPa	122.6MPa	39.3MPa	81.6MPa	76.7MPa	58.6MPa	79.8MPa	61.1MPa	41.1MPa	54.8MPa

Table F11.a - Maximal Von Mises criteria by span for each of the twelve checking points.

	top flange				web top		bottom flange				flanges middle
Span	right above	left above	right below	left below	right	left	right above	left above	right below	left below	above	below
1	0.594	0.401	0.552	0.368	0.183	0.334	0.371	0.318	0.385	0.332	0.174	0.265
2	0.618	0.439	0.61	0.446	0.143	0.297	0.279	0.213	0.29	0.222	0.15	0.199

Table F11.b - Maximal Von Mises ratio by span for each of the twelve checking points.

	top flange				web top		bottom flange				flanges middle
	right above	left above	right below	left below	right	left	right above	left above	right below	left below	above	below
Stress	8.4m	8.4m	8.4m	8.4m	6.0m	6.0m	2.1m	2.7m	2.1m	2.7m	2.1m	2.1m
ULS-STR	11	4	11	4	8	8	12	8	12	8	8	8
Crane	8.4m	8.4m	8.4m	8.4m	4.2m	4.2m	2.1m	0.9m	2.1m	0.9m	2.1m	2.1m

Table F11.c - Position of stress, ULS combination and position of crane for the maximal rate of each of the twelve control points.

F12 - Transverse buckling of the flanges §6.3

EN1993-1-1 (6.60 + 6.61)

F121 - Top flange

Combination for the maximal work rate: ULS-STR 11

Span	N_Ed	M_z,Ed	k_c	L_cr,z	λ_f	N_cr,z	k_fl	χ_z	C_m,z	k_zz	Ratio	Section position	Crane position
1	174.5kN	15.0m.kN	0.82	4.92m	0.995	1309.6kN	1.1	0.543	0.964	1.048	0.691	2.7m	2.7m
2	89.7kN	9.3m.kN	0.82	3.28m	1.018	1049.0kN	1.102	0.529	0.971	1.022	0.681	8.4m	8.4m

Table F121 - Maximal buckling ratio by span for top flange.

F122 - Bottom flange

Combination for the maximal work rate: ULS-STR 12

Span	N_Ed	M_z,Ed	k_c	L_cr,z	λ_f	N_cr,z	k_fl	χ_z	C_m,z	k_zz	Ratio	Section position	Crane position
1	135.2kN	1.9m.kN	0.91	5.46m	1.466	362.3kN	1.147	0.326	0.935	1.086	0.585	6.0m	2.4m
2	134.4kN	1.9m.kN	0.752	3.008m	0.808	1194.0kN	1.081	0.657	0.959	1.042	0.358	6.0m	2.4m

Table F122 - Maximal buckling rate by span for bottom flange.

F13 - Local buckling §6.6
F131 - Local buckling of the flanges EN1993-1-5 §4

EN1993-1-5 (4.14)
Combinations for the maximal work rates: ULS-STR 8 (top flange), ULS-STR 8 (bottom flange)

	top flange					bottom flange
Span	M_y	W_el,y	Ratio	Section position	Crane position	M_y	W_el,y	Ratio	Section position	Crane position
1	71.1m.kN	1288.1cm³	0.202	2.1m	2.1m	-36.3m.kN	977.8cm³	0.136	5.7m	2.1m
2	40.0m.kN	1121.3cm³	0.131	8.6m	6.8m	-49.9m.kN	964.6cm³	0.188	6.2m	2.4m

Table F131 - Maximal local buckling ratio by span for each flange.

F132 - Local buckling of the web under shear EN1993-1-5 §5

EN1993-1-5 (5.10)
Combination for the maximal work rate: ULS-STR 1

Span	k_τ	h_w/t_w	lim_max	σ_E	τ_cr	λ_rel,w	χ_w	Ratio	Section position	Crane position
1	5.352	41.825	66.299	h_w/t_w < lim_max : La vérification n'est pas nécessaire
2	5.368	41.825	66.395	h_w/t_w < lim_max : La vérification n'est pas nécessaire

Table F132 - Maximal local buckling ratio by span for the web under shear.

F133 - Local buckling of the web under point load EN1993-1-5 §6

EN1993-1-5 (6.14)
Combination for the maximal work rate: ULS-STR 1

Span	F_Ed;	s_s	F_cr	λ_rel,F	χ_F	L_eff	Ratio	Section position	Crane position
1	41.4kN	0.075m	1737.0kN	0.563	0.888	0.222m	0.085	5.7m	3.9m
2	41.4kN	0.075m	1739.3kN	0.563	0.888	0.223m	0.085	7.0m	5.1m

Table F133 - Maximal local buckling ratio by span for the top of the web under point load.

F134 - Interactions EN1993-1-5 §7

EN1993-1-5 (7.2)
Combination for the maximal work rate: ULS-STR 8

Span	η₂	η₁	Ratio	Section position	Crane position
1	0.085	0.202	0.246	2.1m	2.1m
2	0.085	0.131	0.189	8.6m	6.8m

Table F134.a - Maximal local buckling interaction ratio by span under point load.

si EN1993-1-5 (7.1)
Combinations for the maximal work rates: ULS-STR 1 (top flange), ULS-STR 1 (bottom flange)

				top flange				bottom flange
Span	η₃	W_f,Rd	W_pl,Rd	η₁	Ratio	Section position	Crane position	η₁	Ratio	Section position	Crane position
1	0.0	η₃ ≤ 0.5 : La vérification n'est pas nécessaire
2	0.0	η₃ ≤ 0.5 : La vérification n'est pas nécessaire

Table F134.b - Maximal local buckling interaction ratio by span under shear.

F2 - Serviceability Limit States

Limiting values of horizontal deflections (EN1993-6 7.1) : L/600
Limiting values of vertical deflections (EN1993-6 7.2) : L/600
Limiting values for web breathing (EN1993-6 §7.4(3)) : b/t_w < 120
Limiting values for vibration of the bottom flange (EN1993-6 §7.6(2)) : L_f / i_f,z ⩽ 250

Combinations for the maximal deflection rates: SLS 6 (vertical), SLS 4 (horizontal)

	SLS _z		SLS _y		Web breathing	Vibration of the bottom flange
Span	Abscissa	Ratio	Abscissa	Ratio	Ratio	Ratio
1	2.7m	0.378	3.0m	0.843	0.349	0.56
2	8.2m	0.16	8.2m	0.89	0.349	0.373

Table F2 - Maximal SLS ratios and associate positions by span for each axis.

F3 - Conclusion

Maximum work rate: 89.0%, the section is correct.