BC-1

1
Combined Bending Axial Forces (BEAM COLUMNS)
Chap. (8)
Members subjected to combined axial loads and
bending moments are called Beam-Columns.
Examples of this, are floor or roof beams
resisting later wind loads. Top chord truss
elements supporting roof loading causing bending,
etc.
Interaction Formula
where Pu factored axial
compression. Mu factored bending
moment. Pn nominal axial strength.
Mn nominal bending strength.
BC-1
2
LRFD Criteria for Beam Column
Equation (BC-1) is the basic of AISC design
criteria as stated in (chapter H) of AISC LRFD
specs-
BC-2
3
LRFD Criteria for Beam Column
Example BC-1
The beam-column shown in Figure below is pinned
at both ends and is subjected to the factored
loads shown. Bending is about the strong axis.
Determine weather this member satisfy the
appropriate AISC Specification interaction
equation.
Solution From the column load tables (Table
4.1) the axial compressive design strength of
W8x58 with Fy50 ksi and KyLy17 ft
?cPn 286 kips
BC-3
4
LRFD Criteria for Beam Column (Contd.)
From the beam design charts (Table 3-10 page 3
125) for un braced length of Lb17, and Cb1.0
?bMn 202 k.ft.
For this condition and this loading Cb1.32
(table 3.1)
? ?bMn 1.32 x 202 267 k.ft. ?bMp
224 k.ft. (Table 3.2 page 3-18). ? ?bMn 224
k.ft. ? ?bMp
This member satisfies the AISC specifications.
BC-4
5
Moment Amplification
Moments caused by eccentricity of axial load
cannot be ignored for beam-columns.
The value of (P?) is called Moment
magnification due to initial beam column initial
crookedness or from bending due to transverse
load (?).
It can be proven that a beam column with
initial crookedness (e) and initial moment (Mo
Pu e), that the total moment becomes
M Pu ( e ymax)
BC-5
6
Moment Magnification Contd.
where- M Magnified moment. Mo Initial
moment (due to initial crookedness or more often
due to transverse loads).
Example BC-2
Compute the amplification factor for example
(BC-1)
So M 1.15 Mo 1.15 ? 93.5
107.5 kft.
BC-6
7
Braced Frames Unbraced Frames

• Moment amplification is covered in chapter C of
  the AISC code.
• Two amplification factors are used in LRFD-
• One to account for amplification due to
  deflection.
• One to account for amplification due to frame
• sideway to lateral forces in unbraced
  frames.

LRFD account for both effects
Mu Mr B1 Mnt B2 Mlt AISC C2-1a
Where Mr Mu factored load combination as
affected by amplification. Mnt Maximum moment
assuming no sidesway (no translation) Mlt
Maximum moment caused by sidesway (lateral
translation). (Mlt 0 for braced
frames) B1 amplification factor for braced
frames. B2 amplification factor for unbraced
frames.
BC-7
8
Members in Braced Frames
The maximum moment in a beam-column depend on the
end bending moments in a braced frame, the
various cases are accounted for by a factor (Cm)
as follows
(AISC C2-2)
BC-8
9
Evaluation of Cm Factor
Where
Cm Coefficient whose value taken as follows
1 If there are no transverse loads acting on
the member,
(AISC Equation C2 4)
M1/M2 is a ratio of the bending moments at the
ends of the member. M1 is the end moment that is
smaller in absolute value, M2 is the larger, and
the ratio is positive for moment bent in reverse
curvature and negative for single-curvature
bending. Reverse curvature (a positive ratio)
occurs when M1 and M2 are both clockwise or both
counterclockwise.
BC-9
10
Evaluation of Cm Factor
2. For transversely loaded members, Cm can be
taken as 0.85 if the ends are restrained against
rotation and 1.0 if the ends are unrestrained
against rotation (pinned). End restraint will
usually result from the stiffness of members
connected to the beam-column. The pinned end
condition is the one used in the derivation of
the amplification factor hence there is no
reduction for this case, which corresponds to Cm
1.0. Although the actual end condition may lie
between full fixity and a frictionless pin, use
of one of the two values given here will give
satisfactory results.
(AISC C2 5)
BC-10