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
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
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
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
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
xZ 88 3in
xZ 98 3in
xZ 186 3in
xZ 12 3in
xZ 24 3in
xZ 36 3in
xZ 72 3in
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
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
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
(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
LATERAL SUPPORT OF STEEL BEAMS
47 kip-ft
28.5 kip-ft
CASE II
W10X12
CASE IIICASE I
CASE II CASE IIICASE I
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'
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
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'
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
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
• 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
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
wu = 1.242 kips/ft
Mu2
8uw L 21.242x30
8= = = 139.7 ft-kips CASE 1
139.7
STRENGTH OF W14 X 26= 150.7 ft-kips
STRENGTH OF W16 X 26= 165.7 ft-kips
Page # 3-127
Page # 1-22
Page # 1-23
Page # 1-20
SELECT W16X26
SHAPE AREA
W 14x26 7.69 245
W16x26 7.68 301
XI
Page # 1-21
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” =
Page # 3-211
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
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.
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.
Details of web opening in steel girders for HVAC ducts.
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