Recommendations for verifying lateral stability of precast beams in transitory phases

KRAHL, P. A.; LIMA, M. C. V.; EL DEBS, M. K.

doi:10.1590/S1983-41952015000600003

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Articles • Rev. IBRACON Estrut. Mater. 8 (6) • Nov-Dec 2015 • https://doi.org/10.1590/S1983-41952015000600003 copy

Recommendations for verifying lateral stability of precast beams in transitory phases

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

This paper presents recommendations for security check of precast beams in transitory phases, compare results of parametric analyzes with national and international code recommendations and confront the formulations used for the calculation of critical load of lateral instability. In transport and lifting phases, precast beams are susceptible to loss lateral stability because the established supports provides little restriction to the element rotate on its principal axis and move laterally. To recommend limits of slenderness, parametric analysis are performed using formulations based on bifurcacional instability, including eigenvalue problems with the finite element method. The results show that the safety limits for I beams and rectangular beams are different. For the analyzed cases and with reference to beam slenderness equation used by fib Model Code [13], the limit determined for rectangular beams would be 85 and for I beams 53, which could be taken as 50, as recommended by the code. Within the analyzed cases of I beams, only the fib Model Code [13] recommendation attend the slenderness limit for transitory phases.

Keywords :
lateral instability of beams; precast concrete; lifting; transport; slenderness

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E-mail: arlene@ibracon.org.br

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[TFN1] ℓ_0f: theoretical span or spacing between lateral restraints;

[TFN2] h: section height;

[TFN3] b_f: compressed flange width. For rectangular section change b_f for b_w;

[TFN4] h_m: distance between the center of gravity and the support point;

[TFN5] a: elastic beam lateral displacement, considering the self-weight acting laterally.

[TFN6] Notes¹ do not distinguish between transitory and permanent phases ² As the current version do not contemplate the subject, it is being done reference to previous version.

Code	Slenderness limit
Code	Permanent phase	Transitory phase
Eurocode 2 [11]	ℓ_0f h^1/3 / b_f^4/3 < 50 h / b_f < 2,5	ℓ_0f h_1/3 / b_f^4/3 < 70 h / b_f < 3,5
ABNT NBR 9062 [9]²	ℓ_0f h / b_f² < 500 ℓ_0f / b_f < 50	h_m / a > 2
ACI 318-02 [12]¹	ℓ_0f / b_f < 50
fib Model Code [13]¹	ℓ_0f h_1/3 / b_f^4/3 < 50
BS:8110-1 [14]¹	ℓ_0f h / b_f² < 250 ℓ_0f / b_f < 60
ABNT NBR 6118 [10]¹	h / b_f < 2,5	ℓ_0f / b_f < 50

g(α)	ϱ=a/ℓ
g(α)	0,5	0,6	0,7	0,8	0,9	1
0,02	2,55	2,4	0,133	0,018	0,0043	0,0014
0,04	10,1	9,23	0,523	0,0716	0,0171	0,0056
0,08	40	31,8	1,95	0,278	0,0672	0,0222
0,16	150,1	83,5	6,28	1	0,253	0,0854
0,32	485,3	148,4	14,8	2,93	0,83	0,297
0,6	1079,5	193,1	23,8	5,76	1,89	0,751
1,2	1833	222,4	31,7	8,9	3,34	1,48
2,5	2396,5	238,4	36,7	11,2	4,57	2,19
5	2678,2	245,9	39,3	12,5	5,29	2,63
10	2817,1	249,7	40,7	13,2	5,68	2,88
20	2885,3	251,6	41,4	13,5	5,89	3,02
40	2919,7	252,5	41,7	13,7	6	3,09
100	2944,4	253,5	42	13,9	6,07	3,16

Rectangular beam		I-section beam
Width (cm)	Height (cm)	Span (m)	Flange width (cm)	Height (cm)	Span (m)
15 a 50	150	30	40 a 80	150	30
20	150	20 a 30	80	150	30 - 40

h / b_w	ℓ_0f h^1/3 / b_w^4/3	Buckling load (kN/m)
		Lebelle		Stratford et al.		Stratford et al.¹		LTBeam
		I²	T	I	T	I	T	I	T
10,00	430,89	4,07	10,62	3,82	10,24	3,73	9,87	10,45	11,51
7,50	293,62	9,55	18,43	9,14	24,28	8,61	23,40	17,61	19,64
5,00	171,00	31,5	35,37	31,13	81,96	25,78	79,00	34,14	38,38
3,75	116,52	72,75	53,63	74,13	194,30	49,70	187,20	53,32	60,09
3,00	86,53	138,30	60,48	145,17	379,45	74,06	365,63	74,9	84,50

Vão (m)	ℓ_0f h^1/3 / b_w^4/3	Buckling load (kN/m)
		Lebelle		Stratford et al.		Stratford et al.¹		LTBeam
		I²	T	I	T	I	T	I	T
20	293,62	9,55	18,43	9,14	24,28	8,61	23,79	17,61	19,34
25	244,68	23,20	29,49	24,83	41,96	22,03	41,03	37,00	31,20
30	195,74	77,80	51,50	96,30	81,96	71,94	79,93	50,40	55,78

Slenderness ratio	Item 3.1	Item 3.2
ℓ_0f h_1/3 / b_w^4/3	85	195
ℓ_0f h / b_w²	180	750
ℓ_0f / b_w	60	100
h / b_w	3	7,5

h / b_f	ℓ_0f h^1/3 / b_f^4/3	Buckling load (kN/m)
		Lebelle		Stratford et al.		Stratford et al.¹		LTBeam
		I²	T	I	T	I	T	I	T
3,75	116,52	15,56	23,97	17,89	27,18	16,3	26,25	23,80	25,96
2,50	67,86	51,2	41,4	53,3	50,61	41,5	48,04	41,24	45,65
1,88	46,24	105,97	62,29	122,5	82,19	78,6	76,4	63,24	69,29

Esbeltez	fib Model Code [13]	NBR9062 [9]	ACI 318-02 [12]	BS:8110-1 [14]	Eurocode 2 [11]	Item 3.3	Item 3.4
ℓ_0f h^1/3 / b_f^4/3	50	-	-	-	70	70	53
ℓ_0f h / b_f²	-	500	-	250	-	125	82
ℓ_0f / b_f	-	50	50	60	-	50	43
h / b_f	-	-	-	-	3,5	2,5	1,88

Vão (m)	ℓ_0f h^1/3 / b_f^4/3	Buckling load (kN/m)
		Lebelle		Stratford et al.		Stratford et al.¹		LTBeam
		I²	T	I	T	I	T	I	T
30	46,24	105,97	62,3	121,84	82,2	78,14	76,36	63,24	69,29
35	53,95	45,40	42,10	55,40	51,75	42,20	48,25	42,25	46,12
40	61,66	23,73	29,86	28,93	34,67	24,27	32,4	29,7	32,31