剖面模数计算方法

Allowable stress to ABS MODU 2001, part 3, charpter 2, section 1, item 3.3
F=Fy/F.S., where
Fy = 235 N/mm2 , or 34 ksi
F.S. = 1.67 for axial or bending stress
2.50 for shear stress
Hence, F = 140.7 N/mm2 , or 20.4 ksi for axial or bending stress
94.0 N/mm2 , or 13.6 ksi for shear stress
1. Bulkhead
1.1 Wind pressure p = f V k
2.c h.c s N/m2where
f = 0.611
Vk = 100 knots = 51.44 m/s
c s = 1.0
c h = 1.1
hence p = 1778.4 N/m2or 37.13 lbf/ft2
1.2 Bulkhead plating
Plate panel maximum size (mm)4070 by 690
Plate thickness, t (mm)8
Bulkhead load to wind pressure p = 1778.4 N/m2or 37.13 lbf/ft2
Stress due to lateral perpendicular load:σ = kpb2/t2 where
k = 0.741 for panel size ratio of 5.9 (4070/690)
p =37.13lbf/ft2, or0.26 lbf/in2
b =690 mm
t =8mm
Henceσ =1421 lbf/in2, or 1.42ksi OK
3
Shear stress at support,τ = RF max/A web = 4.49N/mm2, or0.7ksi OK
2. Bottom
2.1. bottom plating
Plate panel maximum size (mm)2650 by 830
Plate thickness, t (mm)8
Deck load to MODU 2001, w920 kgf/m2, or 188 lbf/ft2
Stress due to lateral perpendicular load:σ = kwb2/t2 where
k = 0.718 for panel size ratio of 3.19 (2650/830)
w =188lbf/ft2, or 1.31 lbf/in2
b =830mm
t =8mm
Henceσ =10090 lbf/in2, or10.1ksi OK
3
3. APV' lower Supporting Structure
As per contract specification 2.22G, foundations for equipment shall be designed for combined static
and dynamic load of 1.5g vertical and 0.5g horizontal for roll and pitch.
According to HYDRALIFT Drawing: T2820-D1157-G0040 APV's arrangement,
per WORKING APV' average weight: 2750kg,
add 10% variables: 3025kg is to be used in following calculation.
3.1 check supporting plate panel
The supporting plate panel, which is supported at four sides, is considered conservatively as plate beam supported at two longer edges.
Plate panel concentrated load maximum size (mm)1420 by 760
Plate thickness, t (mm) =25.5
Deck load to MODU 2001, w =920kgf/m2, or 188 lbf/ft2
Max moment due to deck load q: M q =qL/8 =925N.m
where L =0.76m
Max reaction force due to deck loa R q=qL/2=4870N
Load Case 1 (LC1): Heave at 1.5g
Force due to static and dynamic load:P = ma,where
m=3025kg
a=14.7m/s2 (1.5g)
P=44467.5N
Hence,Q=2P = 88935N
M1max=Ql1l2/L=16605N.m
where L=0.76m
l1=0.33m
l2=0.43m
R1max=Ql2/L=50318N
Force due to pitch:P=ma,where
m=3025kg
a= 4.9m/s2 (0.5g)
P pitch=14822.5N
Hence,Q2=2.755*P/5.76 = 7090N
The force acts on plate as a longitudinal tension, as illustrated in sketch
LC3: Roll at 0.5g to starboard
Force due to roll:P=ma,where
m=3025kg
a= 4.9m/s2 (0.5g)
P=14822.5N
Hence,Q2=2.755*P/5.76 = 7090N
The force acts on plate as a transverse tension, as illustrated in sketch
LC4: Heave at 1.5g, pitch at 0.5g to forward and roll at 0.5g to starboard (LC1+LC2+LC3)
moment:BM max=M1max + Mq =17530N.m
shear:RF max=R1max + Rq =55188N
longitudinal tension:TF x =14179N
transverse tension:TF y =14179N
plate beam modulus:SM=bt2/6 =154cm3
where b =142cm
t = 2.55cm
plate beam area:A1 =bt =362cm2
A2 =at =194cm2
where a =76cm
Bending stress,σ = BM max/SM =113.91N/mm2, or16.5ksi OK Shear stress,τ = RF max/A1 = 1.52N/mm2, or0.2ksi OK Longitudinal tension stress:σx = TF x/A2 =0.73N/mm2, or0.1ksi OK Transverse tension stress:σy = TF y/A1 =0.39N/mm2, or0.1ksi OK
3.2 Check supporting structure
where L= 1.42m
BM max = (q1+q2)L2/8 =1774kgf.m
RFmax = (q1+q2)L/2 = 4997kgf
3
Bending stress ,σ = BM max/SM = 6.21N/mm2, or0.9ksi OK Shear stress ,τ = RF max/A1 = 6.81N/mm2, or 1.0ksi OK
b. Beam A2-B2
Similar to beam A1-B1, check beam A2-B2 stress is OK.
R B2 =4964kgf
c. Beam A3-B3
Similar to beam A1-B1, check beam A3-B3 stress is OK.
R B3 =2697kgf
d. Beam A4-B4
Similar to beam A1-B1, check beam A4-B4 stress is OK.
R B4 =2482kgf
e. Beam A5-B5
Similar to beam A1-B1, check beam A5-B5 stress is OK.
R B5 =4964kgf
f. Beam A6-B6
Similar to beam A1-B1, check beam A6-B6 stress is OK.
R B6 =4964kgf
g. Beam A7-B7
Similar to beam A1-B1, check beam A7-B7 stress is OK.
R B7 =4964kgf
h. Beam A8-B8
Similar to beam A1-B1, check beam A8-B8 stress is OK.
R B8 =4964kgf
i. Beam A9-B9
Similar to beam A1-B1, check beam A4-B4 stress is OK.
R B9 =2482kgf
j. Beam C1-D1
Similar to beam A1-B1, check beam C1-D1 stress is OK.
R C1 =4989kgf
R D1 =4989kgf
k. Beam C2-D2
Similar to beam A1-B1, check beam C2-D2 stress is OK.
R C2 =4957kgf
R D2 =4957kgf
l. Beam C3-D3
Similar to beam A1-B1, check beam C2-D2 stress is OK.
R C3 =2690kgf
R D3 =2690kgf
3.2.2 Check transverse girders
Max moment due to force R B1: M B1 = 0.76*1.985*R B1/2.745 =2746kgf.m
Max moment due to force R B2: M B2 = 1.42*1.325*R B2/2.745 =3402kgf.m
Max moment due to force R B3: M B3 = 2.08*0.665*R B3/2.745 =1359kgf.m Combined moment: BM max =6163kgf.m
Reaction force: R E1 = 1.985*R B1/2.745 + 1.325*R B2/2.745 + 0.665*R B3/2.745 =6663kgf Reaction force: R F1a = 0.76*R B1/2.745 + 1.42*R B2/2.745 + 2.08*R B3/2.745 =5995kgf hence,RF max =6663kgf
Bending stress ,σ = BM max/SM =24.00N/mm2, or 3.5ksi OK Shear stress ,τ = RF max/A WEB =8.17N/mm2, or 1.2ksi OK
n. Beam E2-F2
Similar to beam E1-E1, check beam E2-F2 stress is OK.
Reaction force: R F2 =5984kgf
Distributed load along the beam length due to bulkhead weight, q = 660kgf/m
Max moment due to load q: M q =qL2/8 =622kgf.m
Max moment due to force R D1: M D1 = 0.76*1.985*R D1/2.745 =2742kgf.m
Max moment due to force R D2: M D2 = 1.42*1.325*R D2/2.745 =3398kgf.m
Max moment due to force R D3: M D3 = 2.08*0.665*R D3/2.745 =1355kgf.m
Combined moment: BM max =6774kgf.m
Reaction force: R E3 =7558kgf
Reaction force: R F3a =6890kgf
hence,RF max =7558kgf
Bending stress ,σ = BM max/SM =26.38N/mm2, or 3.8ksi OK Shear stress ,τ = RF max/A WEB =9.27N/mm2, or 1.3ksi OK
Deck load to MODU 2001, w = 920kgf/m2 or 188 lbf/ft2
Distributed load along the beam length, q = 0.165*w =151.8kgf/m
Max moment due to load q: M q =q*1.4452*(1+1.3/2.745)2/8 =86kgf.m
Max moment due to force R B4: M B4 = 1.445*1.3*R B4/2.745 =1699kgf.m
Max moment due to force R B5: M B5 = 2.105*0.64*R B5/2.745 =3402kgf.m
Combined moment: BM max =4259kgf.m
Reaction force: R F1b =2424kgf
Reaction force: R =5146kgf
thk(cm)width(cm)
section
area(cm2)
ctr.dist. to
plt top(cm)
d(cm)I0 (cm4)
mom. of
inert.(cm4)
SM(cm3)
top flg 2.5516.542.075 1.27522.844135.0
web1808042.5542666.748997.3
btm flg0.816.513.282.950.732077.6 Combined135.27533.7125210.02520 Bending stress ,σ = BM max/SM =16.58N/mm2, or 2.4ksi OK Shear stress ,τ = RF max/A WEB = 6.31N/mm2, or0.9ksi OK
Deck load to MODU 2001, w = 920kgf/m2 or 188 lbf/ft2
Distributed load along the beam length, q1 = 0.165*w =151.8kgf/m
Distributed load along the beam length due to bulkhead weight, q2 = 660kgf/m BM max = (q1+q2)L2/8 =765kgf.m
RFmax = (q1+q2)L/2 = 1114kgf
Hence,R =1114kgf
Bending stress ,σ = BM max/SM = 2.98N/mm2, or0.4ksi OK Shear stress ,τ = RF max/A WEB = 1.37N/mm2, or0.2ksi OK
r. Beam E5-F5
Similar to beam F3-E5, check beam E5-F5 stress is OK.
Reaction force: R E5b =1185kgf
R F5 =1185kgf
Deck load to MODU 2001, w = 920kgf/m2 or 188 lbf/ft2
Distributed load along the beam length, q = 0.165*w =151.8kgf/m
Max moment due to load q: M q =q*0.832*(1+2.66/3.49)2/8 =41kgf.m
Max moment due to force R B6: M B6 = 0.68*2.81*R B6/3.49 =2718kgf.m
Max moment due to force R B7: M B7 = 1.34*2.15*R B7/3.49 =4098kgf.m
Max moment due to force R B8: M B8 = 2.0*1.49*R B8/3.49 =4239kgf.m
Max moment due to force R B9: M B9 = 2.66*0.83*R B9/3.49 =1570kgf.m
Combined moment: BM max =9829kgf.m
Reaction force: R E4b =9779kgf
Bending stress ,σ = BM max/SM =38.27N/mm2, or 5.6ksi OK Shear stress ,τ = RF max/A WEB =11.99N/mm2, or 1.7ksi OK
3.2.3 Check longitudinal girders
Deck load to MODU 2001, w = 920kgf/m2 or 188 lbf/ft2
Distributed load along the beam length, q = 0.3*w =276kgf/m
Max moment due to load q: M q =q*3.5882/2 =1777kgf.m
Max moment due to force R F1a +R F1b: M F1 = 0.938*(R F1a+R F1b) =7897kgf.m
Max moment due to force R F2: M F2 = 2.193*R F2 =13123kgf.m
Max moment due to force R F3a +R F3b: M F1 = 3.588*(R F3a+R F3b) =29041kgf.m
Combined moment: BM max =51838kgf.m
Reaction force: R G1 = q*3.588 + RF1a + RF1b + RF2 + RF3a + RF3b=23397kgf
Bending stress ,σ = BM max/SM =167.46N/mm2, or24.3ksi OK Shear stress , 1.2τ = RF max/A WEB =65.58N/mm2, or9.5ksi OK
Deck load to MODU 2001, w = 920kgf/m2 or 188 lbf/ft2
Distributed load along the beam length, q1 = 0.3*w =276kgf/m
Load as Heave at 1.5g
Force due to static and dynamic load:P = ma,where
m=3025kg
a=14.7m/s2 (1.5g)
P=44468N
Hence,q2=2P/L = 6384kgf/m
where L= 1.42m
Max moment due to load q1: M q1 =q1*4.072/2 =2286kgf.m
Max moment due to load q2: M q2 =q2*1.422/2 =6437kgf.m
Max moment due to force R E4a +R E4b: M E4 = 1.42*(R E4a+R E4b) =21194kgf.m
Max moment due to force R E5a +R E5b: M E4 = 4.07*(R E5a+R E5b) =9357kgf.m
Combined moment: BM max =39273kgf.m
Reaction force: R G2 = q1*4.07 +q2*1.42 + R E4a + R E4b + R E5a + R E5b=27413kgf hence,RF =27413kgf
Bending stress ,σ = BM max/SM =65.74N/mm2, or9.5ksi OK Shear stress ,τ = RF max/A WEB =26.89N/mm2, or 3.9ksi OK
v. Beam G3-F5
Deck load to MODU 2001, w = 920kgf/m or 188 lbf/ft2
Distributed load along the beam length, q1 = 0.165*w =151.8kgf/m
Distributed load along the beam length due to bulkhead weight, q2 = 660kgf/m Max moment due to load q1: M q1 =q1*4.072/2 =1257kgf.m
Max moment due to load q2: M q2 =q2*4.072/2 =5466kgf.m
Max moment due to force R F4: M F4 = 1.42*R F4 =10964kgf.m
Max moment due to force R F5: M F5 = 4.07*R F5 =4823kgf.m
Combined moment: BM max =22510kgf.m
Bending stress ,σ = BM max/SM =62.18N/mm2, or9.0ksi OK Shear stress ,τ = RF max/A WEB =11.26N/mm2, or 1.6ksi OK
4. APV' Upper Supporting Structure
3.1 :P pitch =14822.5N
Q1pitch =7733N Load due to a APV's Roll at 0.5g to starboard has calculated as 3.1 :P roll =14822.5N
Q1roll =7733N 4.1 Check APV' end box mounting structure on forward transverse bulkhead
4.1.1 Check stiffener' flange subjected to tension
As per "Yield Line Analysis of Bolted Hanging Connections", AISC, Engineering Journal, Vol.14, No.3 1977, For hanger rods, the allowable working load is the smaller of following :
P1 = F y t b2(2r)1/2(1+a/b)/LF
P2 = F y t b2[r(1+a/b)]1/2/LF
where F y=235N/mm2
t b=13mm
r= (F y-F b)/F y =0.401
F b=140.7N/mm2
a=50mm
b=35.5mm
LF = 1.7
P1 =50388N
P2 =22959N
hence,the allowable total force carried by flange[ P ]=22959N
maximal load forced on stiffener L100x75x13 is P max = 1.5Q1roll = 11600 N < [ P ]OK!
4.1.2 Check stiffener subjected to compression
R max =8522N9
thk(cm)plt width
/sect dep
(cm)
section
area(cm2)
ctr.dist. to
plt top(cm)
d(cm)I0 (cm4)
mom. of
inert.(cm4)
SM(cm3)
att plt0.85644.80.4 2.493.9
section-7.515.46 5.9794.6359.7
Combined60.26 1.8453.670
4.3in3 Bending stress ,σ = BM max/SM =23.83N/mm2, or 3.5ksi OK
R max=R F =8738N
thk(cm)plt width
/sect dep
(cm)
section
area(cm2)
ctr.dist. to
plt top(cm)
d(cm)I0 (cm4)
mom. of
inert.(cm4)
SM(cm3)
att plt 1.2519.2240.625 3.1196.0
section-7.521.06 6.6994.6314.4
Combined45.06 3.5510.396
5.9in3
Bending stress ,σ = BM max/SM =22.61N/mm2, or 3.3ksi OK Shear stress ,τ = RF max/A1 = 4.15N/mm2, or0.6ksi OK
C. Check beam L-M
R max =11934N
thk(cm)width(cm)
section
area(cm2)
ctr.dist. to
plt top(cm)
d(cm)I0 (cm4)
mom. of
inert.(cm4)
SM(cm3)
top flg00000.00.0
web0.9 2.5 2.25 1.25 1.2 4.8
btm flg0.97.5 6.75 2.950.5 1.7
Combined9 2.5 6.53
0.2in3 Bending stress ,σ = BM max/SM =4145.20N/mm2, or601.6ksi OK Shear stress ,τ = RF max/A1 =53.04N/mm2, or7.7ksi OK
4.2 Check APV' end box mounting structure on inboard longitudinal bulkhead
As per "Yield Line Analysis of Bolted Hanging Connections", AISC, Engineering Journal, Vol.14, No.3, 1977, For hanger rods, the allowable working load is the smaller of following :
P1 = F y t b2(2r)1/2(1+a/b)/LF
P2 = F y t b2[r(1+a/b)]1/2/LF
where F y=235N/mm2
t b=19mm
r= (F y-F b)/F y =0.401
F b=140.7N/mm2
a=50mm
b=35.5mm
LF = 1.7
hence,P1 =107634N
P2 =49042N
hence,the allowable total force carried by flange[ P ]=49042N
maximal concentrated load forced on girder T 811x12.5w P max = 3Q2roll = 23199 N < [ P ]OK!
4.2.2 Check longitudinal girder' web stability under compression when roll to starboard
As per "Manual of STEEL CONSTRUCTION Allowable Stress Design", AISC,
Slenderness ratio Kl/r =450> 200
where K =2
l =811mm
r = 3.61mm
And C c =(2*3.142E/F y)1/2 =130
where E =200000Mpa
F y =235N/mm2
here,Kl/r >C c
hence,the allowable stress F a = 12*3.142E/(23*(Kl/r)2 = 5.08N/mm2
Compression total load forced on Girder' web section Q =12*Q2roll92796N web section area A=19625mm2
RF max =92796N
thk(cm)width(cm)
section
area(cm2)
ctr.dist. to
plt top(cm)
d(cm)I0 (cm4)
mom. of
inert.(cm4)
SM(cm3)
top flg 2.5547.3120.615 1.27565.474578.2
web 1.2581.1101.37543.155563.784757.5
btm flg 1.911.521.8584.6 6.674705.9
Combined243.8426.1234041.73939
240.4in3 Bending stress ,σ = BM max/SM =17.91N/mm2, or 2.6ksi OK Shear stress ,τ = RF max/A web =9.15N/mm2, or 1.3ksi OK
4.3 Check supporting APV' end box mounting structure on TF-12 transverse bulkhead
Bending stress ,σ = BM max/SM =72.79N/mm2, or10.6ksi OK Shear stress ,τ = RF max/A web =17.26N/mm2, or 2.5ksi OK
thk(cm)width(cm)
section
area(cm2)
ctr.dist. to
plt top(cm)
d(cm)I0 (cm4)
mom. of
inert.(cm4)
SM(cm3)
top flg 1.310130.65 1.8871.8
web 1.3 6.28.06 4.425.8184.0
btm flg 1.957.5109.258.4532.948.7
web 1.2581013.453.3262.1
top flg 1.25121518.025 2.01270.1
Combined155.318.8302636.7269
16.4in3
Bending stress ,σ = BM max/SM =74.44N/mm2, or10.8ksi OK Shear stress ,τ = RF max/A web =17.26N/mm2, or 2.5ksi OK。