plastic sectional modulus
DESCRIPTION
PLASTIC SECTIONAL MODULUS . Shape Property, Independent of material Higher indicates more bending strength. PNA. PNA. PNA. TOTAL. PNA (Plastic Neutral Axis). TOTAL. PNA (Plastic Neutral Axis). FULLY LOADED. FORCE X LEVERARM. For rectangular sections=. FORCE X LEVERARM. - PowerPoint PPT PresentationTRANSCRIPT
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PLASTIC SECTIONAL MODULUS
3x in(z ),
• Shape Property, Independent of material• Higher indicates more bending strength
i ix A Yz
1 1 2 2x A Y A Yz
12x0.5 12x0.5
xZ 12 3in
12x1 12x1
xZ 24 3in
xZ
1 1 2 2x A Y A Yz
6 6
1y 0.5"
2y 0.5"
1A 12 2in
2A 12 2in
1A 12 2in
2A 12 2in
1y 1"
2y 1"
PNA
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x 12x1.5 12x1.5z
xZ 36 3in
x 12x3 12x3z
xZ 72 3in
1y 3"
18 18 36 36
2y 3"
1A 12 2in
2A 12 2in
1A 12 2in
2A 12 2in
1y 1.5"
2y 1.5"
PNA
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i ix A Yz
4 41 1 2 2 3 3x A Y A Y A Y A Yz
8x4.5 4x2 4x2 8x4.5 36 8 8 36
xZ 88 3in
PNA
4A 8 2in
1A 8 2in2A 4 2in
3A 4 2in
1y
4y
2y
3y
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4 41 1 2 2 3 3xZ A Y A Y A Y A Y
PNA(Plastic Neutral Axis)
41 2 3A A A A A TOTAL
10 2 2 10 24
10x4.5 2x2 2x2 10x4.5 45 4 4 45
98 3in
2in1
y
4y
2y
3y
1A 10 2in2A 2 2in
3A 2 2in
4A 10 2in
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41 2 3A A A A A TOTAL
10 2 2 10 24 2in
4 41 1 2 2 3 3xZ A Y A Y A Y A Y
10x8.5 2x4 2x4 10x8.5 85 8 8 85
186 3in
PNA(Plastic Neutral Axis)
1y
4y
2y
3y
1A 10 2in
2A 2 2in
3A 2 2in
4A 10 2in
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xZ 88 3in
xZ 98 3in
xZ 186 3in
xZ 12 3in
xZ 24 3in
xZ 36 3in
xZ 72 3in
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FULLY LOADED
yf2
bd
2
yf2
bd
2
1 d3 2
2 d3 2
yf yf
(INT )M FORCE X LEVERARM
2y
y
f bd 2d bdx f2 2 3 6
(INT )M y xf .S
xS For rectangular sections=2bd
6
2 d3 2
1 d3 2
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yf bd2
(INT )M FORCE X LEVERARM
2
y ybd d bdf x f2 2 4
(INT )M y xf .Z i ix A Yz
yf bd2 yf bd
2
yf bd2
yf yf
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i ix A Yz
1 1 2 2A Y A Y
bd d bd d. .2 4 2 4
2 2 2bd bd bd8 8 4
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(INT )M y y8F x9 4F x4
M y y72F 16F
M y88F
M x yZ F xZ 88 3in
SECTION ELEVATION
y8F
y4F
y8F
y4F
y4F y4F
y8F y8F
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LATERAL SUPPORT OF STEEL BEAMS
47 kip-ft
28.5 kip-ft
CASE II
W10X12
CASE IIICASE I
CASE II CASE IIICASE I
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CASE I if lateral brace is spaced 0-2.75’CASE II if lateral brace is spaced 2.75’-8’CASE III if lateral brace is spaced more than 8’
W10X12
CASE I
Design Moment Strength = = 47 kip-ft NM
BRACING DISTANCE
BRACES
W10X12
b0 L 2.75'
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CASE II
Design Moment Strength reduces as increasesbL
AT b 2.75 'LAT b 'L 8
NM 47kip-ft
NM 28.5 kip-ft
Linear variation in & bL NM
W10X12b2.75' L 8'
LATERAL BRACES
bL
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bL
AT b 'L 8AT b 'L 18
NM 28.5
NM 8.25
Design Moment Strength reduces as increases
Should be avoided for load bearing floor beams.
kip-ft
kip-ft
CASE III
bL
bL 8'
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CASE I CONSTRUCTION DETAILS
bL 0
x
xX-X
CONCRETE
W-SHAPE STEEL STUDS
Most Common Current Practice Using Metal Deck and Shear Studs. Steel and Concrete Deck can be designed as Composite or Non-Composite
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Use 50 ksi and select a shape for a typical floor beam AB. Assume that the floor slab provides continuous lateral support. The maximum permissible live load deflection is L/180. The service dead loads consist of a 5-inch-thick reinforced-concrete floor slab (normal weight concrete), a partition load of 20 psf, and 10 psf to account for a suspended ceiling and mechanical equipment. The service live load is 60 psf.
yF
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• Fy = 50ksi
• Case 1
•
• LIVE LOAD = 60psf
LL
• DEAD LOADS 1) 5” Slab
2) Partition = 20psf
3) Ceiling, HVAC = 10psf
GIRDER
GIRDER
(PRIMARY BEAMS)
not to exceed 180
L
Figure 1
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DESIGN LOAD (kips/ft) on AB = wu x TRIBUTORY AREA LENGTH OF BEAM
1.2x(62.5 20 10) 1.6(60) x[6x30]30
[ ] x1
1000= 1.242 kips/ft
12” of Slab = 150 psf6” of Slab = 75 psf1” of Slab = 12.5 psf5” of Slab = 62.5 psf(12.5 psf for every inch of concrete thickness)*5 x 12.5 = 62.5
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wu = 1.242 kips/ft
Mu2
8uw L 21.242x30
8= = = 139.7 ft-kips CASE 1
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139.7
STRENGTH OF W14 X 26= 150.7 ft-kips
STRENGTH OF W16 X 26= 165.7 ft-kips
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SELECT W16X26
SHAPE AREA
W 14x26 7.69 245
W16x26 7.68 301
XI
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EXTRA SELF WEIGHT MOMENT = 21.2x0.026x30
8= 3.3 ft-kips
MOMENT STRENGTH APPLIED MOMENT 165.7 139.7 + 3.3
W16X26 is OK
CODE 30x12
180
360180
ACTUAL45
384
wl
EI= = = 2” =
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w =(60)x(6x30)
30= 360 lb/ft
0.36012
45x0.03x(30x12)384x29,000x301
= 0.360 kips/ft
= 0.03 kips/in
= = 0.75” 2” OK
= 45
384wl
EI;
.kipsin
4( )in
2 .kipsin
2inin
= in 4( )in
=
kips/in
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Typical Copes for a shear connection of a large girder to column web.
Note that duct holes have to be strengthened by plates. Also, holes are at third point where shear & moment are not maximum.
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Cantilever construction for projected balcony.
If shear studs are noticed on beams and column then those members have to be encased in concrete for increasing fire resistance of steel.
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Details of web opening in steel girders for HVAC ducts.