Beams

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25 Νοε 2013 (πριν από 4 χρόνια και 1 μήνα)

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Beams


BEAMS

A structural member loaded in the
transverse direction to the longitudinal
axis.

Internal Forces:

Bending Moments and Shear

Beam Shapes

Section Properties AISC Section I

y
w
f
t
h
970


W
-

(eg W44x335)

Most commonly Used/Wide Flange I, pp 1
-
10:1
-
27


S
-

(eg S24x121)

pp. 1
-
30:1
-
31


M
-

(eg M12x11.8)

pp. 1
-
28:1
-
29


Channels (eg C15x50)

pp. 1
-
34:1
-
39

Beams

y
w
f
t
h
970

Plate Girders

Structural Steel
-

Sections

Built Up members

I Shapes

H Shapes

Box Shapes


Fillet Welding
of Web to
Flange Plates
Fillet Welding
of Web to
Flange Plates
Beams

Depending on the use they are referred to as:

Joists

Support Floor Deck

Floor Beams

Beams that support joists

Girders:

Support most load in a floor system

Lintels

Over Windows and Door Openings

Support portion of wall above opening

28
.
6
15
.
9
50
000
,
29
38
.
0
38
.
0




y
p
F
E

Beams

Purlins

Support Roof Surface

Roof Beams

Support Purlins

Spandrel Beams

Support outside edges of
a floor deck and outside
walls of buildings

Depending on the use they are referred to as:

Structural Steel
-

Characteristics

Buckling:

Instability due to slenderness



Elastic Buckling


Limit States


Load Deflection
0
50
100
150
200
250
300
350
400
450
500
0
4
8
12
16
20
24
Deflection (in)
Load (kips)
FEM
Test

Limit States




Limit States

Limit States

Limit States


Flexure


Elastic


Plastic


Stability (buckling)


Shear


Deflection


Fatigue


Supports

Flexure

u
n
b
M
M


Elastic

Plastic

Stability (buckling)

a
b
n
M
M


LRFD

ASD

90
.
0

b

67
.
1


b
Flexure
-

Elastic

I
My
f

S=I/c : Section Modulus (Tabulated Value)

S
M
I
c
M
f
max
max
max



Example

Compute M
y

Flexure
-

Plastic

Flexure
-

Plastic

Z=(0.5A)a : Plastic Section Modulus (Tabulated Value)


M
p
= A
c
f
y
= A
t
f
y
= f
y
(0.5A) a = M
p
=Zf
y


M
p/
M
y
=Z/S

For shapes that are symmetrical about the axis of bending the plastic and elastic
neutral axes are the same

C=T

A
c
f
y
=A
t
f
y

A
c
=A
t

Example

Compute M
p

Example

Flexure
-

Stability

M
p

is reached and section becomes fully plastic


Or


Flange Local Buckling (FLB) Elastically or Inelastically

Web Local Buckling (WLB) Elastically or Inelastically


Lateral Torsional Buckling (LTB) Elastically or Inelastically


A beam has failed when:

Flexure
-

Stability

Slenderness Parameter

FLB



=b
f
/2t
f

WLB



=h/t
w

LTB



= L
b

/r
y

t
f

b
f

t
w

h

L
b

Flexure
-

Stability

FLB and WLB (Section B5 Table B4.1)

Evaluate Moment Capacity for Different


FLB



=b
f
/2t
f

WLB



=h/t
w

Compact

Non

Compact

Slender

M
p

M
r


p


r

Slenderness Parameter
-

Limiting Values

AISC B5 Table B4.1
pp 16.1
-
16

Slenderness Parameter
-

Limiting Values

AISC B5 Table B4.1
pp 16.1
-
17

Slenderness Parameter
-

Limiting Values

AISC B5 Table B4.1
pp 16.1
-
18

Flexure
-

Stability

FLB and WLB (Section B5 Table B4.1)


FLB



=b
f
/2t
f

WLB



=h/t
w

Compact

Non

Compact

Slender

M
p

M
r


p


r

Example

The beam shown is a W16X31 of A992 steel. It supports a reinforced
concrete slab that provides continuous lateral support of the compression
flange. Service dead load is 450 lb/ft (does not include weight of beam).
Service live load is 550 lb/ft. Does the beam have adequate moment
strength?

Example

Determine Nominal Flexural Strength

Flange Compactness

28
.
6
2

f
f
t
b
28
.
6
15
.
9
50
000
,
29
38
.
0
38
.
0




y
p
F
E

Flange Compact

Web Compactness

8
.
62
25
.
0
7
.
15


w
t
h
8
.
62
55
.
90
50
000
,
29
76
.
3



p

Web Compact

Example

Shape is compact and continuously supported => Plastic Hinge Forms

Nominal Flexural Strength



ft.kips

225


kips
-
in

700
,
2
0
.
54
50





x
y
p
n
Z
F
M
M
lb/ft

481
31
450



D
w
Moment Demand

lb/ft

550

L
w
span
-
mid

@

8
2
max
wL
M



kips
-
ft

54.11
8
30
481
.
0
2


D
M


kips
-
ft

88
.
1
6
8
30
55
.
0
2


L
M
Example

LRFD

kips
-
ft

64
1
6
.
1
2
.
1



L
D
u
M
M
M


164
kips
-
ft

203
0
.
225
9
.
0




u
n
b
M
M

OK

ASD

kips
-
ft

0
.
116
88
.
61
54





L
D
a
M
M
M
116
kips
-
ft

135
67
.
1
225





a
b
n
M
M
OK