Stress states caused in chamber of reinforced concrete grain silo by non-centric emptying on large eccentricities

Jolanta Anna Prusiel; Krzysztof Gierej

Open Access

Stress states caused in chamber of reinforced concrete grain silo by non-centric emptying on large eccentricities

Jolanta Anna Prusiel

and

Krzysztof Gierej

| Dec 31, 2018

Studia Geotechnica et Mechanica

Volume 40 (2018): Issue 4 (December 2018)

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Cite

Published Online: Dec 31, 2018

Page range: 282 - 291

Received: Sep 19, 2018

Accepted: Nov 15, 2018

DOI: https://doi.org/10.2478/sgem-2018-0043

Keywords
stress states, reinforced concrete structure, grain silo, non-centric emptying

© 2018 Jolanta Anna Prusiel, Krzysztof Gierej, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Distribution of local pressure in the cylindrical silo chamber.

Non-centric flow channel during emptying and the distribution of pressure on the silo wall, according to Eurocode 1, Part 4 [11].

Distribution of pressure on the perimeter of the silo, taking into account a non-centric flow channel while emptying the wheat silo with a diameter of 10 m: a) rc = 0.25 r, b) rc = 0.4 r and c) rc = 0.6 r.

Calculation model of a free-standing silo with height H = 25 m and diameter dc = 10 m: a) model of the chamber using the finite element method; and b) levels of reference in the silo adopted for the analysis of internal forces.

Values of components of bulk solid pressure on the wall of the silo with diameter dc=10 m and height H=25 m during emptying on large eccentricities e0(2) = 0 . 375 d c : a) Combination I; b) Combination II.

Maps of internal forces during emptying of the silo with the diameter dc = 10 m on a large eccentric taking into account the occurrence of non-centric flow channel with the radius rc,3 = 0.6r (θ c = 22.3o): a) maps of vertical forces, N [kN/m]; b) maps of hoop forces, R [kN/m]; and c) maps of hoop moments, MR [kNm/m].

Diagrams of hoop moments, MR, kNm/m ( z / h c == 0.5 ): 1) G=0.25, 2) G=0.4 and 3) G=0.6.

Diagrams of vertical moments, MN, kNm/m ( z / h c = 0.5 ): 1) G=0.25, 2) G=0.4 and 3) G=0.6.

Diagrams of hoop forces, R, kN/m ( z / h c = 0.5 ): 1) G=0.25, 2) G=0.4 and 3) G=0.6.

Diagrams of moments in the silo wall calculated taking into account the occurrence of the flow channel: a) vertical moments; and b) hoop moments.

Physicomechanical properties of wheat adopted to determine the pressure in the silo chamber according to Eurocode 1, Part 4, Annex E [11].

Properties of bulk solid	Wheat
	Average value	Parameter a	Upper value	Lower value
Unit weight, γ [kN/m³]	-	-	9.0	7.5
Internal friction angle, ϕ_i [°]	30	1.12	33.6	26.8
Concrete wall friction coefficient, μ	0.57	1.16	0.661	0.491
(D3 wall type)
Lateral pressure ratio, K	0.54	1.11	0.599	0.486
Angle of repose, ϕ_r [°]	34
Patch load solid reference factor, C_op	0.5

Classification of silo action assessment class according to - Eurocode 1, Part 4 [11].

Action assessment class	Class description
Action assessment class 3 (AAC3)	Silo with storage volume of >10,000 tons.
	Silo with storage volume of >1,000 tons, with any of the following calculation situations:
	a) non-centric emptying at e₀/d_c > 0.25;
	b) low silos, with the eccentricity of the upper filling cone e_t/d_c> 0.25.
Action assessment class 2 (AAC2)	All silos mentioned in Eurocode 1, Part 4 [11] which are not assigned to a different class.
Action assessment class 1 (AAC1)	Silo with storage volume of <100 tons.

Extreme values of internal forces in the wall of the silo with the diameter dc=10 m emptied on a large eccentric taking into account the occurrence of non-centric flow channel.

Values of internal forces		Level z/h_c
		0.25	0.5	0.75
N [kN/m]	G = 0.25	–97.51	–232.55	–398.24
	G = 0.4	–112.27	–254.48	–433.87
	G = 0.6	–131.26	–308.19	–487.33
R [kN/m]	G = 0.25	101.05	165.67	195.77
	G = 0.4	113.35	173.13	201.99
	G = 0.6	113.5	173.39	205.98
M_N [kNm/m]	G = 0.25	–1.09	–2.31	–2.89
	G = 0.4	–1.7	–3.39	–4.33
	G = 0.6	–2.39	–4.65	–5.58
M_R [kNm/m]	G = 0.25	–5.78	–11.34	–13.89
	G = 0.4	–8.54	–16.34	–19.91
	G = 0.6	–11.47	–20.82	–23.05

Extreme values of internal forces in the wall of the silo with diameter dc=10 m at selected levels from symmetrical pressure, taking into account the local load.

Values of internal forces		Level z/h_c
		0.25	0.75	0.5
N [kN/m]	e₀₍₁₎ = 0.25d_c	-128.93	-267.79	-417.14
	e₀₍₂₎ = 0.375d_c	-137.93	-276.44	-426.79
	e₀₍₃₎ = 0.5d_c	-146.39	-284.68	-431.66
R [kN/m]	e₀₍₁₎ = 0.25d_c	126.82	213.18	228.26
	e₀₍₂₎ = 0.375d_c	139.09	221.04	253.38
	e₀₍₃₎ = 0.5d_c	144.14	232.03	263.44
M_N [kNm/m]	e₀₍₁₎ = 0.25d_c	0.76	2.9	1.46
	e₀₍₂₎ = 0.375d_c	1.83	3.61	3.57
	e₀₍₃₎ = 0.5d_c	2.32	4.61	4.47
M_R [kNm/m]	e₀₍₁₎ = 0.25d_c	4.43	9.05	6.76
	e₀₍₂₎ = 0.375d_c	6.28	10.42	10.61
	e₀₍₃₎ = 0.5d_c	7.31	12.34	12.42

Percentage comparison of values of hoop moments in the silo with the diameter dc=10 m, calculated taking into account the occurrence of flow channel with values calculated on the eccentricity limit e0(1) = 0.25dc.

Level, z/h_c	Values of hoop moments, M_R [kNm/m]
	e₀₍₁₎= 0.25d_c	G=0.25	%	G=0.4	%	G=0.6	%
0.25	4.43	–5.78	30.5	–8.54	92.8	–11.47	158.9
0.5	9.05	–11.34	25.3	–16.34	80.6	–20.82	130.1
0.75	6.76	–13.89	105.5	–19.91	194.5	–23.05	241.0

Parameters specifying the geometry of the flow channel (AAC3 class) for the selected bulk solids for reinforced concrete silo wall (D3 wall category, according to Eurocode 1, Part 4 [11]).

Type of bulk solid	μ_m	a_μ	μ_d	ϕ_im	a_ϕ	ϕ_ig	μ/tan_dϕ_ig	e_c/r			Angle θ_c[°]
								G=0.25	G=0.4	G=0.6	G=0.25	G=0.4	G=0.6
Barley	0.48	1.16	0.410	28	1.14	31.92	0.658	0.790	0.660	0.479	8.9	14.8	24.9
Corn	0.53	1.12	0.470	31	1.14	35.34	0.663	0.789	0.659	0.478	8.5	14.8	24.8
Wheat	0.57	1.16	0.490	30	1.12	33.6	0.738	0.780	0.646	0.461	7.7	13.3	22.3

Data on discretisation of the silo model (finite element method).

Number of elements (panels)	15 (13 wall panels, 1 bottom plate panel, 1 cover plate panel)
Number of distribution nodes	4,030
Standard net dimensions	40 cm × 131 cm
Thickened net dimensions	20 cm × 65 cm
Number of stiff nodes (of edge elements)	48

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Stress states caused in chamber of reinforced concrete grain silo by non-centric emptying on large eccentricities

Article Category: Research Article

Published Online: Dec 31, 2018

Page range: 282 - 291

Received: Sep 19, 2018

Accepted: Nov 15, 2018

DOI: https://doi.org/10.2478/sgem-2018-0043

Keywords
stress states, reinforced concrete structure, grain silo, non-centric emptying

© 2018 Jolanta Anna Prusiel, Krzysztof Gierej, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Physicomechanical properties of wheat adopted to determine the pressure in the silo chamber according to Eurocode 1, Part 4, Annex E [11].

Classification of silo action assessment class according to - Eurocode 1, Part 4 [11].

Extreme values of internal forces in the wall of the silo with the diameter dc=10 m emptied on a large eccentric taking into account the occurrence of non-centric flow channel.

Extreme values of internal forces in the wall of the silo with diameter dc=10 m at selected levels from symmetrical pressure, taking into account the local load.

Percentage comparison of values of hoop moments in the silo with the diameter dc=10 m, calculated taking into account the occurrence of flow channel with values calculated on the eccentricity limit e0(1) = 0.25dc.

Parameters specifying the geometry of the flow channel (AAC3 class) for the selected bulk solids for reinforced concrete silo wall (D3 wall category, according to Eurocode 1, Part 4 [11]).

Data on discretisation of the silo model (finite element method).

Stress states caused in chamber of reinforced concrete grain silo by non-centric emptying on large eccentricities

Article Category: Research Article

Published Online: Dec 31, 2018

Page range: 282 - 291

Received: Sep 19, 2018

Accepted: Nov 15, 2018

DOI: https://doi.org/10.2478/sgem-2018-0043

Keywordsstress states, reinforced concrete structure, grain silo, non-centric emptying

© 2018 Jolanta Anna Prusiel, Krzysztof Gierej, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Physicomechanical properties of wheat adopted to determine the pressure in the silo chamber according to Eurocode 1, Part 4, Annex E [11].

Classification of silo action assessment class according to - Eurocode 1, Part 4 [11].

Extreme values of internal forces in the wall of the silo with the diameter dc=10 m emptied on a large eccentric taking into account the occurrence of non-centric flow channel.

Extreme values of internal forces in the wall of the silo with diameter dc=10 m at selected levels from symmetrical pressure, taking into account the local load.

Percentage comparison of values of hoop moments in the silo with the diameter dc=10 m, calculated taking into account the occurrence of flow channel with values calculated on the eccentricity limit e0(1) = 0.25dc.

Parameters specifying the geometry of the flow channel (AAC3 class) for the selected bulk solids for reinforced concrete silo wall (D3 wall category, according to Eurocode 1, Part 4 [11]).

Data on discretisation of the silo model (finite element method).

Keywords
stress states, reinforced concrete structure, grain silo, non-centric emptying