7/22/2019 Chute Calculation Example

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Chute Verification

CALCULATIONS INPUT

Steel plate properties

Chute steel plate yield stress fy = 250 MPa (ref. SPEC-007-M0004)

Bending reduction factor b = 0,9 (ref. AS 4100-1998 Table 3.4)

Shear reduction factor for weld s = 0,8 (ref. AS 4100-1998 Table 3.4)

Weld nominal tensile stress (E48XX) fuw = 480 MPa (ref. AS 4100-1998 Table 9.7.3.10)

Iron Ore properties

Bulk ore unit weight b = 27 kN/m3 (ref. FUSP-080-M-00004 Table 2.2.1)Bulk ore internal friction angle i = 38 (ref. FUSP-080-M-00004)

Angle of wall friction w = 26 (ref. AS 3774-1996 Table 3.1)

Wall friction coefficient = 0,49 = TAN(w*/180) (ref. AS 3774-1996 Eq. 6.2.3.3)

Chute properties

P555 Head Chute weight Wch = 9 kN (estimated from 087-M-12233)

P555 Transfer Chute weight Wtc = 3,5 kN (estimated from 087-M-12234)

P555 Head Chute blocked volume Vch = 2,8 m3

(estimated from 087-M-12233)

P555 Transfer Chute blocked volume Vtc = 0,9 m3

(estimated from 087-M-12234)

Chute steel plate thickness t = 10 mm (ref. 087-M-12233)

Maximum steel plate unstiffened span Lus = 1000 mm (ref. 087-M-12234)

Unsupported stiffener span Ls = 1140 mm (ref. 087-M-12234)

Stiffener height hs = 85 mm (ref. 087-M-12234)

Stiffener thickness ts = 10 mm (ref. 087-M-12234)

Transfer chute half angle = 17 (ref. 087-M-12234)

Fill height above max. unstiffened span hf = 2500 mm (estimated from 087-M-12233)

Char. dimension of container cross-section r_c = 200 mm (ref. AS 3774-1996 Table 2.2)

Transition point depth below effective surface z = 1600 mm (estimated from 087-M-12233)

Maximum depth below transition point zb = 1500 mm (estimated from 087-M-12233)

Support properties

Number of collaborating supports ns = 4 (estimated from 087-M-12233)

Support depth hb = 235 mm (ref. 087-M-12233)

Support thickness tb = 10 mm (ref. 087-M-12233)

Plate-to-support fillet weld size es = 6 mm Assume minimum fillet one side

STEEL PLATE CALCULATIONS

Initial normal pressure ratio kh = 0,39 = TAN(*/180)/(TAN(*/180)+) (ref. AS 3774-1996 Eq. 6.2.3.3)

Lateral pressure ratio k = 0,35 (ref. AS 3774-1996 Table 6.3)

Characteristic depth zo = 1172 mm = r_c/(*k) (ref. AS 3774-1996 Eq. 6.2.1.1)

Initial normal pressure at transition level pvi = 8246 Pa = b*r_c*(1-EXP(-z/zo))/ (ref. AS 3774-1996 Eq. 6.2.1.1)

Maximum normal pressure pnh = 18782 Pa = kh*(b*zb+pvi) (ref. AS 3774-1996 Eq. 6.2.3.3)

Ultimate moment in steel plate Mup = 2817 N*m/m = 1.2*pnh*(Lus*10^-3)^2/8 Calc'd as simple supported beam

Nominal steel plate moment capacity Mnp = 6250 N*m/m = t^2/4*fy

Steel plate bending check 2,0 > 1,0 OK

STIFFENER CALCULATIONS

Linear load on stiffener qs = 9391 N/m = pnh*Lus*10^-3/2 Assume uniforme pressure

Ultimate moment in stiffener Mus = 1831 N*m = 1.2*qs*(Ls*10^-3)^2/8 Calc'd as simple supported beam

Stiffener slenderness s = 8,5 = hs/ts*SQRT(fy/250) (ref. AS 4100-1998 Clause 5.2.2)

Plasticity limit ep = 8 (ref. AS 4100-1998 Table 5.2)

Yield limit ey = 15 (ref. AS 4100-1998 Table 5.2)

Stiffener section elastic modulus Zs = 12042 mm3

= hs^2*ts/6

Compact section eff. section modulus Zc = 18063 mm3

= hs^2*ts/4

Striffener effective section modulus Ze = 17632 mm3 = Zs+((ey-s)/(ey-ep)*(Zc-Zs)) (ref. AS 4100-1998 Clause 5.2.4)Stiffener nominal moment capacity Mns = 4408 N*m = fy*Ze*10^-3

Stiffener bending check 2,2 > 1,0 OK

SUPPORT CALCULATIONS

Total weight Wt = 112,4 kN = Wch+Wtc+b*(Vch+Vtc)

Ultimate load per collaborating support Vub = 33,72 kN = 1.2*Wt/ns

Nominal weld capacity per support Vnb = 478,6 kN = 0.6*fuw*tb/SQRT(2)*hb*10^-3 (ref. AS 4100-1998 Clause 9.7.3.10)

Support weld check 11,4 > 1,0 OK

b*Mnp/Mup =

b*Mns/Mus =

s*Vnb/Vub =