Storage silo for sugar

Transcription

1 Storage silo for sugar SPECIFICTION Calculate the load on the reinforced concrete circular sugar silo. Literature EN Eurocode 1: ction on structures Part 4: Silos and tanks Geometry of the silo inside dimension (diameter): d c = 4850 mm (axis distance 5 m) height of silo between transition (see point 3 in the following figure) and top of silo: h = 15 m volume: V = h πr 2 = 15 π ( 4,85 2 )2 = 277,12 m 3 thickness of the vertical wall: hopper: cover: 150 mm conical hopper; angle of inclination α = φ r + 5 = 43 ; height of hopper h h = 2,26 m; outlet in the centre; eccentricity of the centre of the outlet e 0 = 0 mm reinforced concrete slab special filling and discharge arrangements: aerated bottom (see Fig. 3.5b in EC1-4) r r+5 Fig.: Left dimensions according to EN ; right the sugar silo height of vertical-walled segment of silo from the transition to the equivalent surface (let s assume the contents sugar could reach the top of silo) h c = h 2 d c 3 2 tgφ r = tg38 = mm 3 2 1

2 overall height of silo from the hopper apex to the equivalent surface h b = h c + h h = tg(38 + 5) = 16000mm 2 ratio of area to perimeter in cross-section of vertical segment of silo: U = r 2 = d c 4 = 4850 = 1210 mm 4 Classification of silos (chap. 5.1): h c = = 2,83 > 2,0 slender silo d c 4850 Stored material: sugar (tab. E.1): unit weight: γ u = 9,5 kn/m 3 (upper char. value) angle of repose: φ r = 38 angle of internal friction: mean value: φ i,m = 32 factor: a ϕ = 1,19 lateral ratio: mean value: K m = 0,5 factor: a k = 1,20 wall friction coefficient: wall type: D3 high friction, raspy wall surface (tab. 4.1) mean value: μ m = 0,56 factor: α μ = 1,07 patch load solid reference factor: C op = 0,6 Classification according the ction ssessment Classes: Silo capacity: Classification (chap. 2.5): V γ = 277,12 0,95 = 263,3 t C2 (action assessment class 2) capacity above 100 t Characteristic values of particulate solids (simplified approach čl ): wall friction coefficient: upper characteristic value: μ u = a μ μ m = 1,07 0,56 = 0,6 lower characteristic value: μ l = μ m /a μ = 0,56/1,07 = 0,52 lateral ratio: upper characteristic value: K u = a K K m = 1,20 0,5 = 0,6 lower characteristic value: K l = K m /a K = 0,5/1,20 = 0,417 angle of internal friction: upper characteristic value: φ i,u = a φ φ i,m = 1,26 32 = 38,08 lower characteristic value: φ i,l = φ i,m /a φ = 32/1,19 = 26,89 Following condition should not be exceed: μ tgφ i upper: μ u = 0,6 < tgφ i,u = tg38,08 = 0,783 OK (we use μ u = 0,6 in further calculation) lower: μ l = 0,52 > tgφ i,l = tg26,89 = 0,507 exceeded! (we use μ l = 0,507 in further calculation) 2

3 1) FILLING loads on vertical walls: Slender silos symmetrical filling load (chap ) Upper characteristic value of unit weight is used for calculation of actions. Values of other properties (μ, K a φ i ) to be used for different wall loading assessment are given below: Sugar silo z = h c = mm γ = 9,5 kn = 9, m3 N mm 3 Definition γ μ K z z 0 U Y J characteristic value of unit weight; characteristic value of coefficient of wall friction for a vertical load; characteristic value of lateral ratio; depth below the equivalent surface of the solid in the full condition; Janssen characteristic depth; plan cross-sectional area of vertical wall segment; internal perimeter of the plan cross-section of the vertical walled segment; Janssen depth variation function. 3

4 1-) Calculation of actions: Maximum normal on vertical wall (μ l, K u and φ l ) φ = φ l = 26,81 K = K u = 0,6 μ = μ l = 0,507 z 0 = 1 Kμ U = mm 0,6 0,507 p h0 = γ K z 0 = 9, , = 0,023 MPa Y J (z = mm) = 1 e z z 0 = 1 e = 0,968 p hf (z = mm) = p h0 Y J (z) = 0,023 0,968 = 0,022 MPa p wf (z = mm) = μ p h0 Y J (z) = 0,507 0,023 0,968 = 0,0111 MPa p vf (z = mm) = p h0 K Y J(z) = 0,023 0,6 0,968 = 0,0366 MPa Filling loads on vertical walls z (mm) Yj(z) p hf (MPa) p wf (MPa) p vf (MPa) friction vertical stress 0 0 0,0000 0,0000 0, , ,0047 0,0024 0, , ,0084 0,0042 0, , ,0113 0,0057 0, , ,0136 0,0069 0, , ,0155 0,0079 0, , ,0170 0,0086 0, , ,0181 0,0092 0, , ,0191 0,0097 0, , ,0198 0,0100 0, , ,0204 0,0103 0, , ,0209 0,0106 0, , ,0212 0,0108 0, , ,0215 0,0109 0, , ,0218 0,0110 0, , ,0220 0,0111 0,0366 The resulting characteristic value of the vertical force (compressive) in the wall n zsk per unit length of perimeter after filling at any depth z: z n zsk = p wf (z)dz = μ p h0 [z z 0 Y J (z)] 0 n zsk (z = mm) = 0,507 0,023 [ ,968] = 113,67 N/mm The resulting force transferred by friction: N wf,k = π d c n zsk = π , = 1732,01 kn The resulting force due to vertical : N vf,k = π d c 2 4 p vf = π , = 675,89 kn 4

5 Total bulk unit weight in silo (hopper is excluded): Control: N tot,k = γ V = γ (π d c 2 4 z) = 9, π = 2411,48 kn N wf,k + N vf,k = 1732, ,89 = 2407,9 kn N tot,k = 2411,48 kn 1-B) Calculation of actions: Maximum frictional traction on vertical wall (μ u, K u a φ l ) φ = φ l = 26,81 K = K u = 0,6 μ = μ u = 0,599 z 0 = 1 Kμ U = ,7 mm 0,6 0,599 p h0 = γ K z 0 = 9, ,6 3366,7 = 0,019 MPa Y J (z = mm) = 1 e z z 0 = 1 e ,7 = 0,983 p hf (z = mm) = p h0 Y J (z) = 0,019 0,983 = 0,0187 MPa p wf (z = mm) = μ p h0 Y J (z) = 0,599 0,019 0,983 = 0,0113 MPa p vf (z = mm) = p h0 K Y J(z) = 0,019 0,6 0,983 = 0,0314 MPa Filling loads on vertical walls z (mm) Yj(z) p hf (MPa) p wf (MPa) p vf (MPa) friction vertical stress 0 0 0,0000 0,0000 0, , ,0046 0,0027 0, , ,0081 0,0048 0, , ,0107 0,0064 0, , ,0127 0,0076 0, , ,0143 0,0085 0, , ,0154 0,0092 0, , ,0163 0,0098 0, , ,0170 0,0102 0, , ,0175 0,0105 0, , ,0179 0,0107 0, , ,0182 0,0109 0, , ,0185 0,0111 0, , ,0186 0,0112 0, , ,0188 0,0112 0, , ,0189 0,0113 0,0314 Control - in depth z n-zsk 119,91 N/mm friction N-wfk vertical N-vfk total sugar weight 1826,98 kn 580,73 kn 2407,71 kn 2411,48 kn 5

6 1-C) Calculation of actions: Maximum vertical load on hopper or silo bottom (μ l, K l a φ u ) φ = φ u = 38,08 K = K l = 0,417 μ = μ l = 0,507 z 0 = 1 Kμ U = ,4 mm 0,417 0,507 p h0 = γ K z 0 = 9, , ,4 = 0,023 MPa Filling loads on vertical walls z (mm) Yj(z) p hf (MPa) p wf (MPa) p vf (MPa) friction vertical stress 0 0 0,0000 0,0000 0, , ,0034 0,0017 0, , ,0062 0,0031 0, , ,0086 0,0044 0, , ,0107 0,0054 0, , ,0125 0,0063 0, , ,0140 0,0071 0, , ,0153 0,0077 0, , ,0164 0,0083 0, , ,0173 0,0088 0, , ,0181 0,0092 0, , ,0188 0,0095 0, , ,0193 0,0098 0, , ,0198 0,0101 0, , ,0203 0,0103 0, , ,0206 0,0105 0,0495 Control - in depth z n-zsk friction N-wfk vertical N-vfk total sugar weight 98,09 N/mm 1494,59 kn 913,80 kn 2408,39 kn 2411,48 kn 6

7 2) DISCHRGE loads on vertical walls: Slender silos symmetric discharge loads (chap ) Symmetrical discharge s p he and p we should be determined as: p he = C h p hf p we = C w p wf where for slender silos in C 2 and C 3 is C h = C 0 = 1,15 C w = 1,10 discharge factor wall frictional traction discharge factor 2-) Calculation of actions: Maximum normal on vertical wall (μ l, K u and φ l ) φ = φ l = 26,81 K = K u = 0,6 μ = μ l = 0,507 7

8 2-B) Calculation of actions: Maximum frictional traction on vertical wall (μ u, K u a φ l ) φ = φ l = 26,81 K = K u = 0,6 μ = μ u = 0,599 Discharge loads on vertical walls z (mm) p he (MPa) p ve (MPa) friction 0 0,0000 0, ,0054 0, ,0096 0, ,0130 0, ,0157 0, ,0178 0, ,0195 0, ,0209 0, ,0219 0, ,0228 0, ,0235 0, ,0240 0, ,0244 0, ,0248 0, ,0250 0, ,0252 0,0122 Discharge loads on vertical walls z (mm) p he (MPa) p ve (MPa) friction 0 0,0000 0, ,0053 0, ,0093 0, ,0123 0, ,0146 0, ,0164 0, ,0178 0, ,0188 0, ,0196 0, ,0202 0, ,0206 0, ,0210 0, ,0212 0, ,0214 0, ,0216 0, ,0217 0, C) Calculation of actions: Maximum vertical load on hopper or silo bottom (μ l, K l a φ u ) φ = φ u = 38,08 K = K l = 0,417 μ = μ l = 0,507 8

9 Discharge loads on vertical walls z (mm) p he (MPa) p ve (MPa) friction 0 0,0000 0, ,0039 0, ,0071 0, ,0099 0, ,0123 0, ,0144 0, ,0161 0, ,0176 0, ,0188 0, ,0199 0, ,0208 0, ,0216 0, ,0222 0, ,0228 0, ,0233 0, ,0237 0,0115 9