Page 286 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch06.qxd 9/29/05 5:15 PM Page 6.8

DESIGN OF BUILDING MEMBERS

6.8 CHAPTER SIX

where (KL/r) o = column slenderness of built-up member acting as a unit
α= separation ratio = h/2r ib
h = distance between centroids of individual components perpendicular to member
axis of buckling, in
a = distance between connectors, in
r ib = radius of gyration of individual angle relative to its centroidal axis parallel to
member axis of buckling, in
In this case, h = 1.03 + 0.375 + 1.03 = 2.44 in and α= 2.44/(2 × 1.13) = 1.08. Assume maximum
spacing between connectors is a = 80 in. With K = 1, substitution in Eq. (6.11) yields

 KL  =  19 85 ×12  2  108 2  80  2
.
.


.
 r  m  166  + 082  11. 2  113  = 150
.
.
+ 08
The elastic critical stress buckling stress, from Eq. (6.8), is
π 2 × 29 000
,
F = = 13 90 ksi
.
e
[( . ×12 1 66] 2
)/ .
19 85
For the determination of the critical stress F cr , since
 KL = 19 85 ×12   E 29 000 
,
.
.
.

 r 167 = 143 5 .  > 471 F y = 471 36 = 133 7 .  

.
π 2 × 29 000
,
F = = 13 90 ksi
.
e 2
143 5 .
The critical stress, from Eq. (6.10), is
F cr = 0.877 × 13.90 = 12.19
From Eqs. (6.6) and (6.7), the design strength is
φP n = 0.90 × 11.7 × 12.19 = 128.4 kips > 107.5 kips OK
6.8 STEEL BEAMS
According to the AISC Specification, the nominal capacity M p (in⋅kips) of a steel section in flexure
is equal to the plastic moment:
(6.12)
M p = ZF y
3
where Z is the plastic section modulus (in ) and F y is the steel yield strength (ksi). However, this
applies only when local or lateral torsional buckling of the compression flange is not a governing cri-
terion. The nominal capacity M p is reduced when the compression flange is not braced laterally for
a length that exceeds the limiting unbraced length for full plastic bending capacity L p . Also, the nom-
inal moment capacity is less than M p when the ratio of the compression-element width to its thick-
ness exceeds limiting slenderness parameters for compact sections. The same is true for the effect of
the ratio of web depth to thickness. (See Chap. 5.)
In addition to strength requirements for design of beams, serviceability is important. Deflection
limitations defined by local codes or standards of practice must be maintained in selecting member
sizes. Dynamic properties or the beams are also important design parameters in determining the
vibration behavior of floor systems for various uses.

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