2cbb63b7-b8b6-49a3-9fb7-745bbd511669 35 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

DESIGN PARAMETERS:

Upper characteristic value of the bulk unit weight:

γ 15 kN m 3^/ * :

Shell plate unit weight:

γ.s 77 kN m 3^/ * :

Angle of repose:

φ.r 41 ° * :

Characteristic dimension of inside of silo:

d.c 4.08 m * :

Height of vertical-walled segment of silo from the transition to the base of top pile:

h.m 6 m * :

Total height of the top pile of solid:

h.tp d.c 2 / φ.r tan * :

h.tp 1.773 m *

Height of hopper from the apex to the transition:

h.h 3.28 m * :

Depth below the equivalent surface of the base of the top pile:

h.o h.tp 3 / :

h.o 0.59 m *

Notwithstanding the above, silos in Action Assessment Class 1 may be designed for the single value of the mean wall friction coefficient μm, the mean lateral pressure ratio Km and the mean internal friction angle φim for the stored particulate solid.

height of vertical-walled segment of silo from the transition to the equivalent surface:

h.c h.m h.o + :

h.c 6.59 m *

Overall height of silo from the hopper apex to the equivalent surface:

h.b h.c h.h + :

h.b 9.87 m *

Mean angle of inclination of hopper wall measured from the horizontal:

α 60 ° * :

Angle of inclination of hopper wall measured from the vertical:

β 90 ° * α - :

β ° 30

e.o d.c / #

e.t d.c / #

Eccentricity of the centre of the top surface pile when the silo is full:

e.t 0 m * :

Eccentricity of the centre of the outlet:

e.o 0 m * :

Maximum eccentricity of the surface pile during the filling process:

e.f 0 m * :

Lateral pressure ratio:

K 0.552 :

characteristic value of coefficient of wall friction for a vertical wall:

μ 0.62 :

Action Assessment Class:

AAC 1 :

Plan cross-sectional area of vertical walled segment:

A π d.c 2^* 4 / :

A 13.074 m 2^*

Internal perimeter of the plan cross-section of the vertical walled segment:

U π d.c * :

U 12.818 m *

Check for code limitations:

h.b d.c / 2.42

h.b d.c / 10 <

OK

h.b 100 <

OK

d.c 60 <

OK

ACTIONS ON THE SILO:

5 Loads on the vertical walls of silos:

5.1 General:

(2)P The loads on silo vertical walls shall be evaluated according to the slenderness of the silo determined according to the following classes:

- slender silos, where 2,0 ≤ hc/dc (except as defined in 3.3); - intermediate slenderness silos, where 1,0 < hc/dc < 2,0 (except as defined in 3.3); - squat silos, where 0,4 < hc/dc ≤ 1,0 (except as defined in 3.3); - retaining silos, where the bottom is flat and hc/dc ≤ 0,4. - A silo with an aerated bottom should be treated as a slender silo, irrespective of its slenderness hc/dc.

Type of the silo:

h.c d.c / 1.62

-->

Intermediate slenderness silo

5.3 Squat and intermediate slenderness silos:

5.3.1 Filling loads on vertical walls:

5.3.1.1 Filling symmetrical load:

Janssen characteristic depth:

z.o 1 K μ * / A U / * :

z.o 2.98 m *

Asymptotic horizontal pressure at great depth due to stored particulate solid:

p.ho γ K * z.o * :

p.ho kPa 24.677

Power in hopper pressure relationship:

n 1 φ.r tan + (1 h.o z.o / - (* - :

n 1.499 -

z 0.65 m * (6.59 m * (1.3 m * range :

Squat silo pressure depth variation function:

Y.R 1 z h.o - z.o h.o - / (1 + (n^- vectorize :

Y.R z 0.65 m * 6.59 m * 1.3 m * range : a z h.o - z.o h.o - / : j 1 z length range Y j el 1 a j el 1 + (n^- : for Y m * 41 line :

p.ho 24677.419355 Pa *

Horizontal pressure after filling:

p.hf p.ho Y.R * :

crappy stuff in there

Wall frictional traction after filling:

p.wf μ p.hf * :

Depth measure used for vertical stress assessment in squat silos:

z.v h.o 1 n 1 + (/ z.o h.o - z z.o + 2 h.o * - (n 1 +^z.o h.o - (n^/ (- (* - vectorize :

p.hf 884.127593 kg s 2^/ * 7958.567199 kg s 2^/ * 12109.743793 kg s 2^/ * 14787.871726 kg s 2^/ * 16633.452521 kg s 2^/ * 17968.625361 kg s 2^/ * 18971.273574 kg s 2^/ * 19746.811436 kg s 2^/ * 20361.264901 kg s 2^/ * 20857.877226 kg s 2^/ * 101 mat

p.wf 548.159108 kg s 2^/ * 4934.311663 kg s 2^/ * 7508.041152 kg s 2^/ * 9168.48047 kg s 2^/ * 10312.740563 kg s 2^/ * 11140.547724 kg s 2^/ * 11762.189616 kg s 2^/ * 12243.02309 kg s 2^/ * 12623.984238 kg s 2^/ * 12931.88388 kg s 2^/ * 101 mat

h.o 0.591115 m *

z.o 2.980365 m *

Y.R 0.035827 m * 0.322504 m * 0.490722 m * 0.599247 m * 0.674035 m * 0.72814 m * 0.768771 m * 0.800198 m * 0.825097 m * 0.845221 m * 101 mat :

h.o 0.591115 :

z.o 2.980365 :

h.o 1 n 1 + (/ - (2.596976

Transit because of the crappy stuff

z.o h.o - (2.38925

z z.o + 2 h.o * - (n 1 +^z.o h.o - (n^/ (

z.v z 0.65 6.59 1.3 range : j 1 z length range Temp j el h.o 1 n 1 + (/ - (z.o h.o - (z j el z.o + 2 h.o * - (n 1 +^z.o h.o - (n^/ (- (* : for Temp m * 31 line :

z.v 0.074858 m * 0.75384 m * 1.247602 m * 1.627484 m * 1.931465 m * 2.181868 m * 2.392787 m * 2.573618 m * 2.730897 m * 2.869332 m * 101 mat

Vertical stress in stored solid after filling:

p.vf γ z.v * :

Characteristic value of vertical stress resultant per unit perimeter in the vertical walled segment:

n.zSk μ p.ho * z z.v - (* :

z m 0.65 1.3 1.95 2.6 3.25 3.9 4.55 5.2 5.85 6.5 101 mat

Y.R 0.04 m * 0.32 m * 0.49 m * 0.6 m * 0.67 m * 0.73 m * 0.77 m * 0.8 m * 0.83 m * 0.85 m * 101 mat

p.hf kPa 0.88 m * 7.96 m * 12.11 m * 14.79 m * 16.63 m * 17.97 m * 18.97 m * 19.75 m * 20.36 m * 20.86 m * 101 mat

p.wf kPa 0.55 m * 4.93 m * 7.51 m * 9.17 m * 10.31 m * 11.14 m * 11.76 m * 12.24 m * 12.62 m * 12.93 m * 101 mat

p.vf kPa 1.12 11.31 18.71 24.41 28.97 32.73 35.89 38.6 40.96 43.04 101 mat

n.zSk kN m / 8.8 8.36 10.75 14.88 20.17 26.29 33.01 40.18 47.72 55.55 101 mat

5.3.1.2 Filling patch load:

(4) For silos of intermediate slenderness (1,0 < hc/dc < 2,0) in Action Assessment Class 1, the filling patch load may be ignored.

h.c d.c / 1.62

AAC 1 :

-->

Patch load ignored

5.3.2 Discharge loads on vertical walls:

5.3.2.1 Discharge symmetrical load:

(6) For intermediate slenderness silos in Action Assessment Class 1, where the mean value of the material properties K and m have been used for design, the discharge factors should be taken as:

Patch load solid reference factor:

C.op 0.5 :

(Table E.1)

Slenderness adjustment factor:

C.S h.c d.c / 1 - :

C.S 0.62

e e.f e.o 12 mat max :

e 0

Discharge factors:

C.h 1 0.15 1.5 1 0.4 e d.c / * + (* C.op * + (C.S * + :

C.w 1 0.4 1 1.4 e d.c / * + (* C.S * + :

C.h 1.55

C.w 1.25

(3) For silos of intermediate slenderness (1,0 < hc/dc < 2,0), the symmetrical discharge pressures phe and pwe should be determined as:

Horizontal pressure during discharge:

p.he C.h p.hf * :

Wall frictional traction during discharge:

p.we C.w p.wf * :

The resulting characteristic value of the discharge vertical force (compressive) in the wall, per unit length of perimeter:

n.zSk C.w μ * p.ho * z z.v - (* :

p.he kPa 1.37 m * 12.37 m * 18.82 m * 22.98 m * 25.85 m * 27.92 m * 29.48 m * 30.69 m * 31.64 m * 32.41 m * 101 mat

p.we kPa 0.68 m * 6.15 m * 9.36 m * 11.43 m * 12.85 m * 13.88 m * 14.66 m * 15.26 m * 15.73 m * 16.12 m * 101 mat

n.zSk kN m / 10.97 10.41 13.39 18.54 25.14 32.76 41.13 50.08 59.47 69.22 101 mat

6 Loads on silo hoppers and silo bottoms:

6.1 General:

6.1.1 Physical properties:

(2)P The loads on the walls of silo hoppers shall be evaluated according to the steepness of the hopper,determined according to the following classes: - a flat bottom shall have an inclination to the horizontal a less than 5°; - a shallow hopper shall be any hopper not classified as either flat or steep; - a steep hopper shall be any hopper that satisfies the following criterion:

β tan 1 K - 2 μ.h * / <

Lower characteristic value of the lateral pressure ratio on the vertical walls:

K 0.55

Lower characteristic value of wall friction coefficient in the hopper:

μ.h 0.58 :

β tan 0.58

1 K - 2 μ.h * / 0.39

0.58 0.39 >

-->

A shallow hopper

6.1.2 General rules:

(2) The mean vertical pressure at the transition between the vertical walled segment and the hopper or on the silo bottom should be determined as:

Bottom load magnifier:

C.b 1.3 :

Mean vertical pressure:

p.vft C.b p.vf * :

p.vft kPa 1.46 14.7 24.33 31.74 37.66 42.55 46.66 50.19 53.25 55.95 101 mat

p.vft 54.74 kPa * :

(7) For each condition in a hopper, the mean vertical stress in the solid at height x above the apex of the hopper should be determined as:

Hopper shape coefficient:

S 2 :

Mobilized or effective wall friction coefficient:

μ.heff 1 K - (2 β tan * / :

μ.heff 0.39

Characteristic value of the hopper pressure ratio:

F 1 0.2 1 β tan + (μ.heff / / (- :

F 0.95

n 0.8 S * μ.heff (β cot * (* :

n 1.08

Vertical coordinate upwards from hopper apex:

x 0 m * 2.5 m * 0.5 m * range :

Mean vertical stress:

p.v γ h.h * n 1 - / (x h.h / (x h.h / (n^- (* p.vft x h.h / (n^* + vectorize :

γ h.h * 49200 Pa *

h.h 3.28 m *

p.vft 54740 Pa *

γ 15000 :

h.h 3.28 :

p.vft 54740 :

gh 49200 :

p.v x 0 2.5 0.5 range : j 1 x length range Temp j el γ h.h * n 1 - / (x j el h.h / (x j el h.h / (n^- (* p.vft x j el h.h / (n^* + : for Temp Pa * 31 line :

p.v 0 20398.960214 kg m s 2^* / * 32307.944356 kg m s 2^* / * 40698.852475 kg m s 2^* / * 46727.38903 kg m s 2^* / * 50959.150296 kg m s 2^* / * 61 mat

Normal pressure on the wall:

p.nf F p.v * :

Frictional traction on the wall:

p.tf μ.heff F * p.v * :

x m 0 0.5 1 1.5 2 2.5 61 mat

p.v kPa 0 20.4 32.31 40.7 46.73 50.96 61 mat

p.nf kPa 0 19.4 30.72 38.7 44.43 48.45 61 mat

p.tf kPa 0 7.53 11.92 15.01 17.24 18.8 61 mat

6.4.3 Discharge loads:

(1) In shallow hoppers under discharge conditions, the normal pressure and frictional traction may be taken as identical to the values on filling.

THICKNESS CALCULATIONS:

Simplified rules for circular silos in Consequence Class 1 shall be applied.

For circular silos with cylindrical walls in Consequence Class 1, this simplified treatment permits a design based only on the ultimate limit state and with a restricted number of load cases being addressed.

Weight of the shell plate:

z W π z * γ.s * U * 4 / :

For

z 1.5 m * :

z 1.5 m *

z W kN m / 1162.74

n.zSk C.w μ * p.ho * z z.v - (* :

n.zSk 28857.89 kg s 2^/ * 32155.97 kg s 2^/ * 36291.81 kg s 2^/ * 41277.56 kg s 2^/ * 47123.55 kg s 2^/ * 53838.78 kg s 2^/ * 61431.2 kg s 2^/ * 69907.99 kg s 2^/ * 79275.67 kg s 2^/ * 89540.21 kg s 2^/ * 101 mat

Vertical membrane stress resultant:

n.xEd