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designing procedure of rectangular steel tank and placing of stiffeners.Descripción completa
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The purpose of this workbook is the design of rectangular tanks with horizontal stiffeners. Reference: "Pressure Vessel Handbook", 8th & 14th Editions and also "Roarkes Formulas for Stress and Strain", 7th Edition Job: Date: By: Description:
Note to sheet user: When using Solver tool solve for the maximum stress in cell B176 equal to to the maximum allowable stress in cell B53 by changing the minimum recommended thickness in cell E126. THIS MUST BE DONE IN ORDER TO ASSURE THE CORRECT THICKNESS IS RECOMMENDED BELOW! V= E= G= H= W= L= S= ta =
134 30,000,000 1.78 72 84.5 50 16,700 0.2500
ft^3 psi
Longest horizontal span between sufficient vertical supports, such as vertical stiffeners, stays or vessel corners.
in INPUT in in Minimum recommended thickness psi t= 0.2500 in in Actual thickness used including corrosion allowance, if applicable. MAKE SURE TO CHANGE THIS TO GET PROPER STIFFENER SIZES! Calculating minimum recommended number of stiffeners based only on tank height 1 Actual number of stiffeners used 2 INPUT
H.1 = H.2 = H.3 =
32.40 in Between top of tank and 1st stiffener 21.60 in Between 1st and 2nd stiffener 18.00 in Between bottom stiffener and tank bottom 0.00 in 0.00 in Calculating distance(s) 'x' from top of tank to each stiffener (lowercase h's in figure above) x.1 = 32.40 in x.2 = 54.00 in x.3 = 72.00 in Tank height 0.00 in 0.00 in Calculating load(s) per inch at each stiffener. Where: w.n = 0.036*G*x.n^2/2 w.1 = 33.63 lb/in w.2 = 93.43 lb/in w.3 = 166.10 lb/in Load at tank bottom 0.00 lb/in 0.00 lb/in Calculating Reactions on each stiffener. Where: R.n = 0.7*w.n R.1 = 23.54 lb/in R.2 = 65.40 lb/in R.3 = 116.27 lb/in Reaction at tank bottom 0.00 lb/in 0.00 lb/in Calculating Minimum Required Moment(s) of Inertia for Stiffener(s). Where: I.n = 1.25*R.n*L^3/E for intermediate stiffeners and I.top = 0.3*w.1*L^4/(192*E*ta) OR I.top = 0.06*w.1*L^4/(192*E*ta), depending on whether intermediate stiffeners are used or not. Below are the smallest size of each structural steel shape that will satisfy the moment of inertia requirement for each stiffener. Required moment of inertia of stiffener(s)
Smallest Single Angle
Smallest CChannel Shape
Smallest Rect. or Square HSS Shape
L2X2X1/8 C3X3.5 HSS2X1X1/8 0.009 in^4 L2X2X1/8 C3X3.5 HSS2X1X1/8 0.123 in^4 L2X2X1/4 C3X3.5 HSS2X1X3/16 0.341 in^4 NA NA NA 0.000 in^4 NA NA NA 0.000 in^4 Calculating pressure(s) at each distance 'x'. Where: P.n = 0.036*G*(x.n-1 + x.n)/2 P.1 = 1.038 psi P.2 = 2.768 psi P.3 = 4.037 psi 0.000 psi 0.000 psi Calculating Required Plate Thickness at each section. Where: t.n = 0.3*MAX(H.n,L)*SQRT(0.036*G*x.n/S) t.1 = 0.167 in Thicknesses calculated based on t.2 = 0.216 in pressure at level n and the longest t.3 = 0.249 in dimension between lines of support. in in Max. thickness = 0.249 in
I.top = I.1 = I.2 =
Smallest WT, MT, or ST Shape
Smallest W, M, S, or HP Shape
ST1.5X2.85 ST1.5X3.75 ST2X4.75 NA NA
M3X2.9 M3X2.9 M3X2.9 NA NA
Maximum deflection of top plate section y(max) = alpha*0.036*G*H.1*L^4/(E*ta^3) y(max) = 0.0035*0.036*1.78*32.4*50^4/(30000000*0.25^3) y(max) = 0.09689 in
Calculating H.1/L to find alpha H.1/L = 0.648 Looking up alpha alpha = 0.00350
Stress and Deflection Calculations below are based on formulas from Roarkes Formulas for Stress and Strain, 7th Ed The top section of plate conforms to Case 10d of Table 11.4, pg 514 Rectangular Plate; three edges fixed, one (a) edge free Uniformly decreasing load from fixed edge to zero at free edge z z Free edge
Free edge
a b x
q a= 50.00 in tr = 0.1974 in Minimum thickness using the solver tool with Roarks b= 32.40 in q= 1.038 psi a/b = 1.54 Formulas (At x = 0, z = 0) sigmaR1 = beta1*q*b^2/tr^2 and Rr.1 = gamma1*q*b (At x = +a/2, z = b if a > b or z = 0.4b if a < b) sigmaR2 = beta2*q*b^2/tr^2 and Rr.2 = gamma2*q*b a/b 0.25 0.50 0.75 1.00 1.50 2.00 3.00 beta1 0.018 0.064 0.120 0.195 0.351 0.507 0.758 beta2 0.019 0.068 0.125 0.166 0.244 0.387 0.514 gamma1 0.106 0.195 0.265 0.324 0.406 0.458 0.505 gamma2 0.075 0.151 0.211 0.242 0.106 0.199 0.313 Calculating beta's and gamma's Calculating stresses and reactions based on the required thickness 'tr' beta1 = 0.351 sigmaR1 = 9818.32 psi beta2 = 0.244 sigmaR2 = 6825.27 psi gamma1 = 0.406 Rr.1 = 13.66 lb/in gamma2 = 0.106 Rr.2 = 3.57 lb/in