1
Developed by Scott CivjanUniversity of Massachusetts, Amherst
Beam – AISC Manual 13th Ed
Beam Members: Chapter F: Flexural Strength Chapter G: Shear Strength Chapter I: Composite Member Strength Part 3: Design Charts and Tables Chapter B: Local Buckling Classification
2
Beam – AISC Manual 13th Ed
Chapter F: Flexural Strength
3
Beam – AISC Manual 13th Ed
b = 0.90 (b = 1.67)
4
Flexural Strength
Beam – AISC Manual 13th Ed
Specification assumes that the following failure modes have minimal interaction and can be checked independently from each other:
• Lateral Torsional Buckling(LTB)• Flange Local Buckling (FLB)• Shear
5
Flexural Strength
Beam – AISC Manual 13th Ed
Local Buckling: Criteria in Table B4.1 Strength in Chapter F: Flexure Strength in Chapter G: Shear
6
Flexural Strength
Beam – AISC Manual 13th Ed
Local Buckling CriteriaSlenderness of the flange and web, , are used as criteria to determine whether buckling would control in the elastic or inelastic range, otherwise the plastic moment can be obtained before local buckling occurs.
Criteria p and r are based on plate buckling theory.
For W-Shapes
FLB, = bf /2tf pf = , rf =
WLB, = h/tw pw = , rw =
yF
E38.0
yF
E76.3
yF
E70.5
yF
E0.1
7
Flexural Strength
Beam – AISC Manual 13th Ed
p “compact” Mp is reached and maintained before local buckling.Mn = Mp
p r “non-compact”Local buckling occurs in the inelastic range.0.7My ≤ Mn < Mp
> r “slender element”Local buckling occurs in the elastic range. Mn < 0.7My
8
Flexural Strength
Local Buckling
Beam – AISC Manual 13th Ed
Mr = 0.7FySx
Mp = FyZx
p
Equation F3-1 for FLB:
r
MnEquation F3-2 for FLB:
Local Buckling CriteriaDoubly Symmetric I-Shaped Members
9
0.7 pfn p p y x
rf pf
M M M F S
0.9 c xn
Ek SM
Note: WLB not shown. See Spec. sections F4 and F5.
Beam – AISC Manual 13th Ed
Mr = 0.7FySx
Mp = FyZx
p
Equation F3-1 for FLB:
r
MnEquation F3-2 for FLB:
Local Buckling CriteriaDoubly Symmetric I-Shaped Members
10
0.7 pfn p p y x
rf pf
M M M F S
0.9 c xn
Ek SM
Note: WLB not shown. See Spec. sections F4 and F5.
Rolled W-shape sections are dimensioned such that the webs are compact and flanges are compact in most cases. Therefore, the full plastic moment usually can be obtained prior to local buckling occurring.
Beam – AISC Manual 13th Ed
The following slides assume: Compact sections Doubly symmetric members and channels Major axis Bending Section F2
11
Flexural Strength
Beam – AISC Manual 13th Ed
Only consider LTB as a potential failure mode prior to reaching the plastic moment.
LTB depends on unbraced length, Lb, and can occur in the elastic or inelastic range.
If the section is also fully braced against LTB, Mn = Mp = FyZx Equation F2-1
When members are compact:
12
Flexural Strength
Beam – AISC Manual 13th Ed
Mp = FyZx Equation F2-1
Mr = 0.7FySx
Lp = Equation F2-5
Lr = Equation F2-6
rts2 = Equation F2-7
ry =
For W shapes c = 1 (Equation F2-8a)ho = distance between flange centroids
A
I y
When LTB is a possible failure mode:
Values of Mp, Mr, Lp and Lr are tabulated in Table 3-2 (pages 3-11 to 3-19)
13
1.76 yy
Er
F2
.71.95 1 1 6.76
0.7y x o
tsy x o
F S hE Jcr
F S h E Jc
y
x
I Cw
S
Equation F2-2
Mr
Mp
Mn
Equation F2-3 and F2-4
Lb
Plastic LTBInelastic
LTB Elastic LTB
Lp Lr
Lb Lateral Brace
M = Constant (Cb=1)
Lateral Torsional Buckling Strength for Compact W-Shape Sections
14
XX
Beam – AISC Manual 13th Ed
Beam – AISC Manual 13th Ed
If Lb > Lr,
Mn = FcrSx ≤ Mp Equation F2-3
Where Equation F2-4
2
02
2
07801π
ts
b
x
ts
b
bcr r
L
hS
Jc.
rL
ECF
If Lp < Lb Lr,
Equation F2-2
Note that this is a straight line.
If Lb Lp, Mn = Mp
Assume Cb=1 for now15
.7 b pn b p p y x p
r p
L LM C M M F S M
L L
Beam – AISC Manual 13th Ed
Results are included only for: • W sections typical for beams• Fy = 50 ksi• Cb = 1
Plots of Mn versus Lb for Cb = 1.0 are tabulated,Table 3-10, pp. 3-96 to 3-131
16
Flexural Strength
Beam – AISC Manual 13th Ed
To compute Mn for any moment diagram,
Mn = Cb(Mn(Cb1)) Mp
Mn = Cb(Mn(Cb1)) Mp
(Mn(Cb1)) = Mn, assuming Cb = 1
Cb, Equation F1-1
0334352
512
max
max .RMMMM.
M.C m
CBAb
17
Flexural Strength
Beam – AISC Manual 13th Ed
Mmax = absolute value of maximum moment in unbraced sectionMA = absolute value of moment at quarter point of unbraced sectionMB = absolute value of moment at centerline of unbraced sectionMC = absolute value of moment at three-quarter point of unbraced
sectionRm = 1.0 for doubly symmetric members or single curvature
XXMA
MB
MCMmax
Shown is the section of the moment diagram between lateral braces.
18
4bL
4bL
4bL
4bL
Flexural Strength
Beam – AISC Manual 13th Ed
X X
XXX
12 5 12.5
1 319.52 5 3 4 32 2
b
. MC .
M M. M M
12.5 12.5
1.673 7.52.5 3 4 34 2 4
b
MC
MM MM
Example
Consider a simple beam with differing lateral brace locations.
Note that the moment diagram is unchanged by lateral brace locations.
19
M
M
X – lateral brace location
Flexural Strength
Beam – AISC Manual 13th Ed
Cb approximates an equivalent beam of constant moment.
X X
Mmax
X X
Mmax/Cb
M
M/2
M
M
M
Cb=1.0
Cb=1.25
Cb=1.67
Cb=2.3
M
20
Flexural Strength
Beam – AISC Manual 13th Ed
Lateral Torsional Buckling Strength for Compact W-Shape SectionsEffect of Cb
Mr
Mp
Mn
LbLp Lr
Cb=1
21
Flexural Strength
Beam – AISC Manual 13th Ed
Lateral Torsional Buckling Strength for Compact W-Shape SectionsEffect of Cb
Mr
Mp
Mn
LbLp Lr
Cb=1
22
Flexural Strength
Cb>1
Beam – AISC Manual 13th Ed
Lateral Torsional Buckling Strength for Compact W-Shape SectionsEffect of Cb
Mr
Mp
Mn
LbLp Lr
Cb=1
23
Flexural Strength
Cb>1
Limited by Mp
Beam – AISC Manual 13th Ed
Chapter G: Shear Strength
24
Beam – AISC Manual 13th Ed
Nominal Shear StrengthVn = 0.6FyAwCv
0.6Fy = Shear yield strength per Von Mises Failure CriteriaAw = area of web = dtw
Cv = reduction factor for shear buckling
25
Shear Strength
Beam – AISC Manual 13th Ed
a = clear distance between transverse stiffenersh = clear distance between flanges minus fillet on a rolled shape
kv limited to 5 if no stiffeners are present, if , or
2
260
wth
ha0.3h
a
Cv depends on slenderness of web and locations of shear stiffeners.It is a function of kv.
25
5
ha
kv
26
Shear Strength
Beam – AISC Manual 13th Ed
For a rolled I-shaped member
If
Then v = 1.00 (= 1.50)
yw FE.t
h 242
Vn = 0.6FyAweb (shear yielding) (Cv = 1.0)
27
Shear Strength
Beam – AISC Manual 13th Ed
Otherwise,for other doubly symmetric shapes
If then
If then
If then
v = 0.9 (=1.67)
y
v
w FEk.t
h 101
y
v
wy
vF
Ek.th
FEk. 371101
y
v
w FEk.t
h 371
1vC
w
y
v
v
th
FEk.
C101
yw
vv
Fth
Ek.C 2
511
28
Beam – AISC Manual 13th Ed
Equation G2-4 Cv reduction0.6FyAw
Vn
Equation G2-5 Cv reduction
y
v
F
Ek.101
y
v
F
Ek.371h/tw
Shear Yielding
Inelastic Shear
Buckling Elastic Shear Buckling
29
0.48FyAw
Shear Strength
Beam – AISC Manual 13th Ed
Deflections : There are no serviceability requirements in
AISC Specification. L.1 states limits “shall be chosen with due
regard to the intended function of the structure” and “shall be evaluated using appropriate load combinations for the serviceability limit states.”
30