28 roark flat plates
TRANSCRIPT
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document.xls
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
1.600
CONSTANTS........................... G_3' -1.67C_1' 0.24 G_3 0.0000
0.42 G_6' 0.62C_1 0.658320 unit G_6 0.0000
G_9' -0.58C_2' 0.40 G_9 0.0000C_2 0.148945
L_3' 0.59C_3' 1.14 -0.56C_3'' -0.87 L_3 0.0050 Figure 28-1 PLAN VIEW OF PLATE/WASHER C_3 0.024992
L_6' 0.26C_4 1.210583 L_6 0.0426
C_5 0.432778 L_9' 0.260.10
C_6' 1.14 L_9 0.2399C_6 0.104596
L_11' 1.79C_7 1.084433 unit L_11'' -4.35
L_11 0.0004C_8' 0.10C_8 0.690564 L_14' 0.80
L_14'' -0.72C_9' 0.64 L_14 0.0051C_9'' 0.15C_9 0.293091 L_17' 0.86
L_17'' 1.52D 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 psiF_1 0.13 k = 1000 Lbs.F_2' 0.97F_2 0.01F_4' 0.63F_4 0.72
F_5 0.11
F_6 0.01
F_7 0.12
F_9' 0.080.00
F_9 0.07
ro
lb/in2
ro / r
lb/in2 =
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document.xls
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
0 logic 1.000 > 1.600 singularity factorr ro
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document.xls
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 -- ContinuedRoark Table 24, Case 2k: Outer edge free, inner edge simply supported… page 342INPUTS FROM ABOVEa 2.400 in radius to outer edgeb 0.880 in radius to inner edge
1.600 in radius to location of w
q_uniform 2371 uniformly distributed load not used in this analysis
t 1.00 in thickness of platev 0.29 unit Poisson ratio 0.88E 29000 ksi Young's modulus of elasticity
2371
0
0 per Roark
0
0
-0.01149 =-q*(a^3)/(D*C7)
0.22204 =(C_9/(2*A*B))*(A^2-RO^2)
-0.00255 radian -0.00255
4310 lb/in shear
( 2,371 /(2 * 0.880 )) * ( 2.400^2 - 1.600^2 ) 2.40
-0.0040 Figure 28-2 PLATE LOADING AND DEFLECTION
0.0006
0.0000
-0.0035 in deflection
Q unit shear lb / inch of circumference
-0.00309 unit applied line moment in-lb / inch of circumference
0.00099 unit radial bending in-lb / inch of circumference
0.00006 unit tangential bending in-lb / inch of radius
-0.00216 radian
r 1.00 in radial location of quantity being evaluated -- input from above
-5231 lb-in/in theta * D * (1 - v^2) /r + v * Mr
-0.00216 * 2,630,314 * (1 - 0.285^2) /1.600 + 0.285 * 0
t 1.0000 in from input aboveS 0.16667
-31
CANTILEVER PLATE COMPARISONq 2371 psiL 1.96 in
M_pl 4554 lb-int_pl 1.00 inS_pl 0.16667
27.32 ksi
ro
lb/in2
yb
Mra
Mrb
Qa
qb'
qb''
qb
Qb
(Q_uniform / (2 * b)) * ( a2 - ro2 )
ya'
ya''
ya'''
ya
qa' Mo
qa'' Mr
qa''' Mt
qa
Mt
in3 1 * t2 / 6
fb k/in2 Mt / S
in3
fb
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document.xls
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
Figure 28-3 CANTILEVERED ANCHOR PLATE
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document.xls
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 -- ContinuedRoark Table 24, Case 1a: Outer edge simply supported, inner edge free … page 335
0.1406
0.00 in -4,267 * 2.40^3 / 2,630,314 * 0.1406
lb/in in^3 / lb-intheta_b' 0.22theta_b -0.001
Mrb' 0.00Mrb 0.00
Qb' 0.00Qb 0.00 lb/in
y' 0.00y'' 0.00y''' 0.00y'''' 0.00y 0.00
theta' 0.00theta'' 0.00theta''' 0.00theta'''' 0.00theta -0.001
Figure 28-4 PLATE LOADING Mr' -266.80Mr'' 0.00Mr''' 0.00Mr'''' 0.00Mr -266.80 lb-in
Mt -1576.45 lb-in tangential moment / inch of circumference MOMENT
S provided 0.1666667 1.0000^3 /6
fb -9459-9.5 ksi
Q =B164*b/r_-W*ro/r_*___*_R_RO_theta_a
Qa -2844.89 lb / inch of circumference SHEAR
Figure 28-5 PLATE LOADING
Mt Mt
yb yb
bending in twisting on plate bending in plate / washer
Figure 28-6 PLATE TWISTING Figure 28-7 PLATE BENDING
yb'
yb
in3/in
lb/in2 /in stress in plate
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document.xls
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 -- 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
Roark, Table 24 Case 10a: Outer edge simply supported … page 363 Figure 28-8 PLATE BENDING DIAGRAM
0 per Roark supported edge
0 simply supported edge
L_11 0.000 from aboveL_17 0.045 from above
-0.0005 in
-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
L/75,994
S_plate 0.167 in^3 b*t^3/6M 616 lb-infb 4 k/in^2
Figure 28-10 VIEW OF PLATE DEFLECTION
ya
Mra
yc -q * a4 /(2 * D) * (L_17 /(1 + v) - 2 * L_11)
Mc q * a2 * L_17 M at center of plate
in3
fb
qa
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Figure 28-1 PLAN VIEW OF PLATE/WASHER row 40
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not used in this analysis
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-0.00216
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lb / inch of circumference
in-lb / inch of circumference
in-lb / inch of circumference
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