ROARK FLAT PLATES EXHAUST STACK ENGINEERING with the SPREADSHEET Copyright 2006 American Society of Civil Engineers A B C D E F G H I J K L 2 FLAT CIRCULAR PLATES / CONSTANT THICKNESS Roark, 5th Edition Table 24 pg 334 a 2.400 in radius to outer edge Check plate bending with several models b 0.880 in radius to inner edge from Roark and Young page 334 1.600 in radius to location of w APPROXIMATE RADIUS OF BOLT HEAD P 42.90 k For allowable P allowed working calculated in the Bolt Group Pullout template trib length 10.05 in ALONG EDGE OF WASHER a 2.400 w 4267 lb/in point load / circumference line load ro 1.600 q_uniform 2371 uniformly distributed load r_ 1.00 in radial location of evaluated quantity b 0.880 t 1.000 in thickness of plate v 0.285 unit poisson ratio E 29000 ksi Young's modulus of elasticity 1.600 CONSTANTS........................... G_3' -1.67 C_1' 0.24 G_3 0.0000 0.42 G_6' 0.62 C_1 0.658320 unit G_6 0.0000 G_9' -0.58 C_2' 0.40 G_9 0.0000 C_2 0.148945 L_3' 0.59 C_3' 1.14 -0.56 C_3'' -0.87 L_3 0.0050 Figure 28-1 PLAN VIEW OF PLATE C_3 0.024992 L_6' 0.26 C_4 1.210583 L_6 0.0426 C_5 0.432778 L_9' 0.26 0.10 C_6' 1.14 L_9 0.2399 C_6 0.104596 L_11' 1.79 C_7 1.084433 unit L_11'' -4.35 L_11 0.0004 C_8' 0.10 C_8 0.690564 L_14' 0.80 L_14'' -0.72 C_9' 0.64 L_14 0.0051 C_9'' 0.15 C_9 0.293091 L_17' 0.86 L_17'' 1.52 D 2630314 lb-in plate constant L_17 0.0451 29,000 * 1.00^3 / ( 12 * ( 1 - 0.285^2) ) * 1000 lb/k F_1' 0.08 psi F_1 0.13 k = 1000 Lbs. F_2' 0.97 F_2 0.01 F_4' 0.63 F_4 0.72 F_5 0.11 F_6 0.01 F_7 0.12 F_9' 0.08 0.00 F_9 0.07 ro lb/in 2 ro / r lb/in 2 =
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ROARK FLAT PLATESEXHAUST STACK
ENGINEERING with the SPREADSHEETCopyright 2006 American Society of Civil Engineers
A B C D E F G H I J K L M
28
FLAT CIRCULAR PLATES / CONSTANT THICKNESS Roark, 5th Edition Table 24 pg 334a 2.400 in radius to outer edge Check plate bending with several modelsb 0.880 in radius to inner edge from Roark and Young page 334
1.600 in radius to location of w
APPROXIMATE RADIUS OF BOLT HEADP 42.90 k For allowable P allowed working calculated in the Bolt Group Pullout templatetrib length 10.05 in ALONG EDGE OF WASHER
a 2.400w 4267 lb/in point load / circumference line load ro 1.600q_uniform 2371 uniformly distributed load
r_ 1.00 in radial location of evaluated quantity b 0.880
t 1.000 in thickness of platev 0.285 unit poisson ratioE 29000 ksi Young's modulus of elasticity
ENGINEERING with the SPREADSHEETCopyright 2006 American Society of Civil Engineers
A B C D E F G H I J K L M
28
FLAT CIRCULAR PLATES / CONSTANT THICKNESS -- ContinuedValues from above for Roark Table 24, Case 1a page …. 362a 2.4 in radius to outer edgero 1.6 in radius to location of wq 2371 lb/in^2
t 1 in thickness of platev 0.285 unit poisson ratioE 29000000 psi Young's modulus of elasticity
-2,371 * 2.400^4 /(2 * 2,630,314) * ( 0.04514 /(1 + 0.285) - 2 * 0.00044)deflection at center of plate
616 lb-in
S 0.1666667
3698 psi shear force
0.0007 radians q/(8*D*a*(1-v)) * (a^2-ro^2)^2
Qa -1580.50 -q/(2*a)*(a^2-ro^2)L/9,374
Figure 28-9 PLATE SUPPORT Roark Table 24, Case 10b: Outer edge fixed supported … page 363ya 0 per Roark supported edgetheta_a 0 fixed edge
L_11 0.000 from aboveL_14 0.005 from aboveL_17 0.045 from aboveyc 0.000 in -q*a^4/(2*D)*(L_14-2*L_11) deflection at center of plateMc 616.37 lb-in q*a^2*L_17 M at center of plateMra -526.832 lb-in -q/(8*a^2)*(a^2-ro^2)^2 M at fixed edge of plate
