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Transcript of Plate Girder - Structural Design Softwareengineering-international.com/PlateGirder.xls ·...
ROJECT : PAGE :
CLIENT : DESIGN BY : JOB NO. : DATE : REVIEW BY :
Plate Girder Design Based on AISC 360-10/16
INPUT DATA & DESIGN SUMMARYSTEEL YIELD STRESS 50 ksi, (345 MPa)SIMPLY SUPPORTED SPAN 72 ft, (21.95 m)SUPERIMPOSED UNIFORM DEAD LOAD 1 klf, (15 kN / m)UNIFORM LIVE LOAD 1 klf, (15 kN / m)POINT DEAD LOAD 60 kips, (267 kN)POINT LIVE LOAD 60 kips, (267 kN)DISTANCE POINT LOAD TO END 24 ft, (7.32 m)
TOP FLANGE WIDTH 16 in ( 406 mm )
TOP FLANGE THICKNESS 1.5 in ( 38 mm )
BOTTOM FLANGE WIDTH 16 in ( 406 mm )
BOTTOM FLANGE THICKNESS 1.5 in ( 38 mm )
WEB THICKNESS 0.5 in ( 13 mm )BEAM DEPTH 53 in ( 1346 mm ) 1/4 x 7 STIFFENER, E. SIDES, AT SUPPORTS ONLY.UNBRACED LENGTH 8 ft, (2.44 m) FLANGE TO WEB WELDING USE 5/16 in - 24 in @ 41 in o.c.
THE GIRDER DESIGN IS ADEQUATE.
ANALYSISCHECK LIMITING WIDTH-THICKNESS RATIOS FOR WEB (AISC 360 Table B4.1)
100.00 < 137.27
> 90.55Noncompact Web
where E = 29000 ksi
137.27
93.26
90.55
50.00 in 50.00 in
6452.1 ft-kips 5824.6 ft-kips
CHECK LIMITING WIDTH-THICKNESS RATIOS FOR FLANGES (AISC 360 Table B4.1)
5.33 < 17.04
< 9.15Compact Flanges
where 17.04
9.15
0.39
1398 1398
35 ksi, (AISC 360 Table note B4.1 & Eq F4-6)
DETERMINE CRITERIA FOR ALLOWABLE FLEXURAL STRENGTH (AISC 360 Table F1.1)
Required ConditionsChapter F Sections
F2 F3 F4 F5Double Symmetric x x
Compact Web x xxNoncompact Web
Slender Web 3806.0 ft-kipsCompact Flanges x ( from following analysis)
Noncompact FlangesSlender Flanges
Applicable Section ok
<== Not Applicable.
13.23 ft
32.74 ft
where 3.75 in 1398
51.50 in 1025
Fy = S =
DL = LL =
PDL =
PLL = c =
bf,top =
tf,top =
bf,bot =
tf,bot =
tw = d =
Lb =
hc / tw = lr =
lp =
lr = 5.7 (E / Fy)0.5 =
lp = (hc / hp) (E / Fy)0.5 / (0.54 Mp / My -0.09)2 = ,for Af,top ≠ Af,bot
lp = 3.76 (E / Fy)0.5 = ,for Af,top = Af,bot
hc = hp =
Mp = My =
0.5 bf,top / tf,top = lr =
lp =
lr = 0.95 (kc E / FL)0.5 =
lp = 0.38 (E / Fy)0.5 =
kc = Min [0.76 , Max (0.35 , 4 / (h / tw)0.5 )] =
Sxt = in3 Sxc = in3
FL =
Mallowable = Mn / Wb =
DETERMINE ALLOWABLE FLEXURAL STRENGTH , Mn / Wb , BASED ON AISC 360 Chapter F2
ry = Sx = in3
h0 = Iy = in4
1.76p yy
EL r
F
2
0
0.7 01.95 1 1 6.760.7 0.7
r ts tsy x y
FE Jc Ey S hxL r rE JcS h FF
(cont'd)
679321 , (AISC 360 F2.2)
38.1458(Use J = 4.03144
4.34 in
1.0 1.0 , (AISC Manual 14th Table 3-1, page 3-10)
586.732 ksi
6452.1 ft-kips
3863.5 ft-kips where 1.67 , (AISC 360 F1)
<== Not Applicable.
7600.9 ft-kips
where 5.33
9.15 17.04
3863.5 ft-kips
9.59 ft
33.05 ft
where 1.04
4.34 in
6452.08 ft-kips
5824.58 ft-kips 5824.58 ft-kips
100.00
93.26 137.27
1.09123
586.577 0.50 > 0.23, AISC 360 F4-5 )
6355.967 ft-kips
Cw = Iy h02 / 4 =
J = [ 2 bf tf3 + (d - tf) tf3] / 3 = in4, (Galambos 1968)
in4 )rts =[( Iy Cw)0.5/ Sx)]0.5 =
c = Cb =
Mallowable, F2 =Mn / Wb = Wb =
DETERMINE ALLOWABLE FLEXURAL STRENGTH , Mn / Wb , BASED ON AISC 360 Chapter F3
l = bf / (2 tf) =
lpf = lp = lrf = lr =
Mallowable, F3 =Min(Mn,F2 , Mn,F3) / Wb =
DETERMINE ALLOWABLE FLEXURAL STRENGTH , Mn / Wb , BASED ON AISC 360 Chapter F4
aw =hc tw/ (bfc tfc) =
Mp = Min [Zx Fy , 1.6Sxc Fy ] =
Myc = Sxc Fy = Myt = Sxt Fy =
l = hc / tw =
lpw = lp = lrw = lr =
ksi, (for Iyc / Iy =
22
20
1 0.078b bcr
tsxb
ts
E JcC LFrS hL
r
, 2
,
0.7 , ,
, ,
p b p
b pp p y p p b rb xn F
r p
cr p r bx
forM L L
L LMin forC SM M F M L L LM L L
Min forSF M L L
, 3
2
0.7 ,
0.9 ,
pfp p y x
rf pfn F
c x
for Noncompact FlangesSM M FM
Ek S for Slender Flanges
l ll l
l
1.1p ty
EL r
F
2
0
01.95 1 1 6.76 Lr t
L xc
E J S hF xcL r E JS hF
, 4.2
,
, ,
, ,
pc yc b p
b ppc yc pc yc L pc yc p b rb xcn F
r p
cr pc yc r bxc
forR M L L
L LMin forC SR M R M F R M L L LM L L
Min forSF R M L L
20
0
1126
fct
w
br
h had dh
, /
1 , , /
pc w pw
ycpc
p p pw pc w pw
yc yc ycrw pw
M for h tM
RM M MMin for h tM M M
l
l ll
l l
22
20
1 0.078b bcr
txcb
t
E JC LFrS hL
r
(cont'd)
6356 ft-kips
1.09123
3806.0 ft-kips
<== Not Applicable.
32.73 ft
50 ksi
50 ksi
1
3487.8 ft-kips
50 100 , 26.5071.4 ft
5.00 0.438
348.131 kips
208.461 kips 1.67 , (AISC 360 G1)
TOTAL SUPERIMPOSED GRAVITY LOAD
w = DL + LL = 2.000 kips / ft , 120.00 kips
CHECK EACH SECTION CAPACITIES
Section Left 0.06 S 0.11 S 0.17 S 0.22 S 0.28 S Point 0.44 S 0.56 S 0.67 S 0.78 S 0.89 S RightDistance 0 4.00 8.00 12.00 16.00 20.00 24.00 32.00 40.00 48.00 56.00 64.00 72.00
53 53 53 53 53 53 53 53 53 53 53 53 5327 27 27 27 27 27 27 27 27 27 27 27 27
37044 37044 37044 37044 37044 37044 37044 37044 37044 37044 37044 37044 37044248.4 248.4 248.4 248.4 248.4 248.4 248.4 248.4 248.4 248.4 248.4 248.4 248.4160.94 151.95 142.96 133.96 124.97 115.97 0.00 31.01 48.99 66.98 84.97 102.96 120.94
0 626 1216 1769 2287 2769 3215 3039 2719 2255 1647 896 0
Mallowable, F4 = Min( Mn,F4.2 , Mn,F4.3, RptMyt) / Wb =
DETERMINE ALLOWABLE FLEXURAL STRENGTH , Mn / Wb , BASED ON AISC 360 Chapter F5
Mallowable, F5 = Min( RpgFySxc , RpgFcr,F5.2Sxc , RpgFcr,F5.3Sxc , FySxt) / Wb =
DETERMINE ALLOWABLE SHEAR STRENGTH , Vn / Wv , BASED ON AISC 360 Chapter G2
h = d - tf,top - tf,bot = in , h / tw = Aw = in2 ,a =
Vn = 0.6 FyAwCv =
Vallowable = Vn / Wv = Wv =
P = PDL + PLL =
d (in)y (in)I (in4)
Wt (plf)V (kips)M (ft-k)
255 , / 3/
5 , / 3v
for a ha hfor a h
k
2
1.0 , / 1.10
1.10 , 1.10 / 1.37/
1.51 , 1.37 //
vw
y
v v vwv
y y yw
v vw
y yw
Ekfor h tF
E E Ek k kfor h th t F F F
E Ek kfor h tF Fh t
C
0.7r t
y
EL r
F
, 5.2
2
2
,
0.3 , ,
, ,
y b p
b py y y p b rb
r p
cr F
by r b
forF L L
L LMin forC F F F L L L
L L
F
ECMin forF L LLbrt
, 5.3
2
,
0.3 ,
0.9 ,
2
y
pfy y
rf pfcr F
c
f
f
for Compact FlangesF
for Noncompact FlangesF F
FEk for Slender Flanges
bt
l ll l
, 10
1 5.7 , 1.01200 300 , 10
w cpg
yw w
Min Ea hMinRMin a t F
, 5.3
2
,
,
0.9 ,
pc yc
pfpc yc pc yc L xc
n F rf pf
c xc
for Compact FlangesR M
for Noncompact FlangesSR M R M FM
Ek S for Slender Flanges
l ll l
l
, /
1 , , /
pc w pw
ytpt
p p pw pc w pw
yt yt ytrw pw
M for h tM
RM M MMin for h tM M M
l
l ll
l l
(cont'd)
3215.08 ft-kips @ 24.00 ft, from heel.
< 3806 ft-kips[Satisfactory]
160.94 kips @ 0.00 ft, from heel.
< 208.461 kips [Satisfactory]
DETERMINE DEFLECTION AT MID SPAN
0.72 in ( L / 1195 ) (for camber, self Wt included.)
where E = 29000 ksi w = 1.248 kips / ftI = 37044 P = 60 kipsb = 0.6 ft L = 72.0 ft
0.58 in ( L / 1482 )
where P = 60 kips w = 1.000 kips / ft
DETERMINE FLANGE TO WEB WELDING (AISC 360 J2.4 )
5/16 in
3/16
7/162.0
160.94 kips
618
2.68 kips / in
A = 24 in 41 in. o.c.
USE 5/16 in - 24 in @ 41 in o.c.
DESIGN STIFFENERS
1. BEARING STIFFENERS ARE REQUIRED AT EACH END SUPPORT. (AISC 360 J10.8)
2. CHECK LOCAL WEB YIELDING FOR THE CONCENTRATED LOAD. (AISC 360 J10.2)R = P = 120.00 kipsN = 0 in, bearing length, point.
1.81 in1.5
26.48 < [Satisfactory]
Mmax =
Mallowable =
Vmax =
Vallowable =
in4
w =wmin = in, < w
wmax = in, > wW =
Vmax =
Q = Af(d - y - 0.5 tf,top) = in3
vmax = Vmax Q / I =
k = tf,top + w =W =
Fy / W
-4000-3500-3000-2500-2000-1500-1000-500
0
BENDING LOADS & CAPACITY
Length
Mom
ents
-250.00-200.00-150.00-100.00
-50.000.00
SHEAR LOADS & CAPACITY
Length
Shea
r For
ces
4 3/ 2225 0.06415
384DLw PbL bL
EI EIL
4 3/ 2225 0.06415
384LLw PbL bL
EI EIL
0.6 0.707
max
EXX w AFBv
W
,5
,2.5
R for c dN kt w
R for c dN kt w
(cont'd)3. CHECK WEB CRIPPLING FOR THE CONCENTRATED LOAD. (AISC 360 J10.3)
2.0
208.57 > P [Satisfactory]
(Note : If item 2, local web yielding is Satisfactory, this item does not need to be checked.)
4. CHECK SIDESWAY WEB BUCKING FOR THE CONCENTRATED LOAD. (AISC 360 J10.4)
49.38 in
960000 ksi
16.461.76
120.00 > P [Satisfactory]
(Note : If item 2, local web yielding is Satisfactory, this item does not need to be checked.)
5. DETERMINE STIFFENER SIZE.
5/8 7 in
11.20[Satisfactory]
11.75 159
R = 160.9 kips
1.67 , (AISC 360 E1)
10.2
113
2751.51 ksi
349.1 kips, (AISC 360 E2)
> R [Satisfactory]
Technical Reference: 1. AISC: "Steel Construction Manual 14th Edition", American Institute of Steel Construction, 2010.
W =
dc = d - 2k =
Cr =
(dc / tw ) / (l / bf) =W =
tw = in , bst =
bst / tw = < 0.56 (E / Fy)0.5 , (AISC 360 Table B4.1)
Ag = in2 , I = in4
Wc =
K l / r = 0.75 h / ( I / Aeff)0.5 =
Cc = 4.71 (E/ Fy)0.5 =
1.52
1.52
0.80 1 3 , 0.5
/ 1 /
0.40 1 3 , 0.5
yw fww
f w
yw fww
f w
tEFN t for c dtd t t
RntEFN t for c dt
d t t
W W
33
2
33
2
/ /0.4 , 1.7/ /
/ // 1 / 1 0.4 , 1.7 2.3/ /
/, 2.3/
r w f c w c w
f f
r w f c w c w
f f
c w
f
C t t d t d tforl lb bh
C t t d t d tforRn l lb bh
d tP forl b
W W W
/ /
,0.658
0.877 ,
F yy cFe
R An c g c
e c
klfor CFr
klfor CFr
W W
2
2/Fe
E
kl r
ROJECT : PAGE :
CLIENT : DESIGN BY : JOB NO. : DATE : REVIEW BY :
Plate Girder Design Based on AISC-ASD 9th, Chapter G
INPUT DATA & DESIGN SUMMARYSTEEL YIELD STRESS 50 ksiSIMPLY SUPPORTED SPAN 72 ftSUPERIMPOSED UNIFORM DEAD LOAD 1 kips / ftUNIFORM LIVE LOAD 1 kips / ft
POINT DEAD LOAD 60 kips
POINT LIVE LOAD 60 kips
TOP FLANGE WIDTH 16 in
TOP FLANGE THICKNESS 1.5 in
BOTTOM FLANGE WIDTH 16 in
BOTTOM FLANGE THICKNESS 1.5 in
WEB THICKNESS 0.5 inBEAM DEPTH 70 in Err:502DISTANCE POINT LOAD TO END 24 ft FLANGE TO WEB WELDING USE 5/16 in - 24 in @ 57 in o.c.UNBRACED LENGTH 8 ft
THE GIRDER DESIGN IS ADEQUATE.
ANALYSIS
1.02
4.16 24.00
11.43 ft
15.84 ft
35.42 ft
30.0 ksi
16.7 ksi
30.0 ksi
33.0 ksi
CHECK WEB SLENDERNESS (AISC-ASD, G1, page 5-51)
71.4 ft, the max clear distance between stiffeners.
134.00 > 132.30 [Satisfactory]
< 282.84
[Satisfactory]
Fy = S =
DL = LL =
PDL =
PLL =
bf,top =
tf,top =
bf,bot =
tf,bot =
tw = d = c = l =
DETERMINE Fb (AISC-ASD, F1.3, page 5-46)
rT = in , Af = in2
a =
h / tw =
76 20000,
/f
cf yy
bMINLd A FF
102000 12000,
0.6 /T
b bu
y f y
C CMAXL rdF A F
3510000
Tb
y
CL r
F
2
1/2 , 0.6
3 1530000Ty
b y yb
lF rMINF F FC
2 2
170000 ,3/ T
ybb
FCMINFl r
312000 , 0.6
/b
b yf
CMINF Fl d A
1 3 3
2 3 3
0.66 ,0.6 ,
, ,
, ,
y c
y c ub
b b u
b b
for lF Lfor lF L L
F MAX for lF F L LMAX for lF F L
22 2 21
22
2 24 411.75 1.05 0.3 1.75 1.05 0.3 22b
M l SM l SCMM S S
760
bF
14000 , 1.5
16.5
2000 , 1.5
yf yf
yf
for a hF F
for a hF
14000 , 1.5
16.5
2000 , 1.5
yf yf
yf
for a hF F
for a hF
(cont'd)DETERMINE ALLOWABLE FLEXURAL STRESS (AISC-ASD G2, pg 5-51)
33.50 0.91
0.999
0.998
32.89 ksi
DETERMINE ALLOWABLE SHEAR STRESS (F4-2, pg 5-49)
67 134
= 5.36 = 0.27
4.65 ksi
TOTAL SUPERIMPOSED GRAVITY LOAD
w = DL + LL = 2.000 kips / ft , 120.00 kips
CHECK EACH SECTION CAPACITIES
Section Left 0.06 S 0.11 S 0.17 S 0.22 S 0.28 S Point 0.44 S 0.56 S 0.67 S 0.78 S 0.89 S RightDistance 0 4.00 8.00 12.00 16.00 20.00 24.00 32.00 40.00 48.00 56.00 64.00 72.00
70 70 70 70 70 70 70 70 70 70 70 70 7035 35 35 35 35 35 35 35 35 35 35 35 35
68848 68848 68848 68848 68848 68848 68848 68848 68848 68848 68848 68848 68848277.3 277.3 277.3 277.3 277.3 277.3 277.3 277.3 277.3 277.3 277.3 277.3 277.3
161.98 152.87 143.77 134.66 125.55 116.44 0.00 30.89 49.11 67.33 85.55 103.77 121.980 630 1223 1780 2300 2784 3232 3057 2737 2272 1660 903 0
4.63 4.37 4.11 3.85 3.59 3.33 0.00 0.88 1.40 1.92 2.44 2.96 3.49
0.00 3.84 7.46 10.86 14.03 16.98 19.71 18.65 16.70 13.86 10.13 5.51 0.00
19.71 ksi @ 24.00 ft, from heel.
< 32.89 ksi[Satisfactory]
Aw = in2 , a = 0.6 Fyw / Fb =
h = d - tf,top - tf,bot = in , h / tw =
P = PDL + PLL =
d (in)y (in)I (in4)
Wt (plf)V (kips)M (ft-k)
fv (ksi)
fb (ksi)
fb,max =
F'b =
-35.00-30.00-25.00-20.00-15.00-10.00
-5.000.00
BENDING STRESS
Length
fb (k
si) &
F'b
(ksi
)
-5.00-4.00-3.00-2.00-1.000.00
SHEAR STRESS
Length
fv (k
si) &
Fv
(ksi
)
'b PGbF F R Re
, 0.42.89
yvyv
C FMIN FF
2
2
5.344.0 , / 1.0/4.05.34 , / 1.0/
v
for a ha h
for a ha h
k
245000 , 0.8
/
190 , 0.8/
v
y wv
v
yw
k for Cvh tF
k for Cvh t F
C
7601 0.0005 , 1.0wPG
f b
hAMINR tA F
312 3, 1.0
12 2
w
fe
w
f
AA
MINRAA
a a
(cont'd)
4.63 ksi @ 0.00 ft, from heel.
< 4.65 ksi [Satisfactory]
DETERMINE DEFLECTION AT MID SPAN
0.40 in ( L / 2173 ) (for camber, self Wt included.)
where E = 29000 ksi w = 1.277 kips / ftI = 68848 P = 60 kipsb = 0.6 ft L = 72.0 ft
0.31 in ( L / 2755 )
where P = 60 kips w = 1.000 kips / ft
DETERMINE FLANGE TO WEB WELDING
5/16 in
3/16
7/16
161.98 kips
822
1.93 kips / in
A = 24 in 57 in. o.c.
USE 5/16 in - 24 in @ 57 in o.c.
DESIGN STIFFENERS
2. CHECK LOCAL WEB YIELDING FOR THE CONCENTRATED LOAD. (AISC-ASD, K3, page 5-81)R = P = 120.00 kipsN = 0 in, bearing length, point.
1.81 in
26.48 < [Satisfactory]
3. CHECK WEB CRIPPLING FOR THE CONCENTRATED LOAD. (AISC-ASD, K4, page 5-81)
206.68 > P [Satisfactory]
(Note : If item 2, local web yielding is Satisfactory, this item does not need to be checked.)
4. CHECK SIDESWAY WEB BUCKING FOR THE CONCENTRATED LOAD. (AISC-ASD, K5, page 5-81)
66.38 in
22.13
120.00 > P [Satisfactory]
(Note : If item 2, local web yielding is Satisfactory, this item does not need to be checked.)
fv,max =
Fv =
in4
w =wmin = in, < wwmax = in, > w
Vmax =
Q = Af(d - y - 0.5 tf,top) = in3
vmax = Vmax Q / I =
1. BEARING STIFFENERS ARE REQUIRED AT EACH END SUPPORT. (AISC-ASD, K1.8, page 5-82)
k = tf,top + w =
0.66Fy
dc = d - 2k =
(dc / tw ) / (l / bf) =
4 3/ 2225 0.06415
384DLw PbL bL
EI EIL
4 3/ 2225 0.06415
384LLw PbL bL
EI EIL
0.3 0.707
max
w AFuBv
,5
,2.5
R for c dN kt w
R for c dN kt w
1.52
1.52
67.5 1 3 , 0.5
34 1 3 , 0.5
yw fww
f w
yw fww
f w
tFN t for c dt d t tR
tFN t for c dtd t t
33
33
6800 / /0.4 , 1.7/ /
6800 / /1 0.4 , 1.7 2.3/ /
/, 2.3/
w c w c w
f f
w c w c w
f f
c w
f
t d t d tforh l lb b
t d t d tR forh l lb b
d tP forl b
(cont'd)
5. DETERMINE STIFFENER SIZE.
5/8 7 in
11.20[Satisfactory]
11.75 159
13.8 ksi
29000 ksi
13.7
107
28.9 ksi, (AISC-ASD, E2, page 5-42)
> [Satisfactory]
Technical Reference: 1. AISC: "Manual of Steel construction 9th", American Institute of Steel Construction, 1990.
tw = in , bst =
bst / tw = < 95 / Fy0.5 , AISC-ASD, B5.1
Aeff = in2 , I = in4
fa =
Es =
K l / r = 0.75 h / ( I / Aeff)0.5 =
Cc = (22Es/ Fy)0.5 =
fa
2
2
3
3
2
2
/1
2,
3 / /53 8 8
12 ,23 /
yc
c
ac c
c
kl rF
C klfor Crkl r kl rF
C CE klfor C
rkl r