Building Design and Construction Handbook - Merritt - Ventech!

8.16 SECTION EIGHT
In 1932, von Karman gave the following formula for determining the effective
width-to-thickness ratio b/t at yielding along the simply supported edges of a thin
rectangular plate subjected to compression between the other two opposite edges:
b/t � 1.9t�E/ƒ (8.3)
y
where b � effective width for a plate of width w, in, and ƒ y � yield strength of
plate material, ksi.
After extensive tests of cold-formed steel structural sections, Winter, in 1947,
recommended that von Karman’s formula be modified to
0.475�E/ƒmax max�
�
b/t � 1.9t�E/ƒ 1 � (8.4)
w/t
where ƒ � maximum stress at simply supported edges, ksi. This formula for
max
determining the effective widths of stiffened, thin, flat elements was first used in
the AISI ‘‘Light-Gage Steel Design Manual,’’ 1949. Subsequent studies showed that
the factor 0.475 was unnecessarily conservative and that 0.415 was more appropriate.
It was used in AISI specifications between 1968 and 1980 to evaluate postbuckling
strength of thin, flat elements.
Until 1986, all AISI specifications based strength of thin, flat elements stiffened
along one edge on buckling stress. In contrast, effective width was used for thin,
flat elements stiffened along both edges. This treatment changed after Pekoz in
1986 presented a unified approach using effective width as the basis of design for
both stiffened and unstiffened elements and even for web elements subjected to
stress gradients. Pekoz proposed the following three equations to generalize Eq.
(8.4) with a factor of 0.415:
� � [1.052(w/t)�ƒ/E]/�k (8.5)
where k � 4.00 for stiffened elements
� 0.43 for unstiffened elements
ƒ � stress in the compression elements of the section computed on the basis
of the design width, in
w � flat width of the element exclusive of radii, in
t � base thickness of element, in
� � a slenderness factor
The effective width is computed from
where � is a reduction factor to be computed from
b � w � � 0.673 (8.6a)
b � �w � � 0.673 (8.6b)
1 � 0.22/�
� � (8.7)
�
These equations were adopted in the AISI ‘‘Specification for the Design of Cold-
Formed Steel Structural Members,’’ 1986 and are retained in the 1996 edition of
the AISI Specifications. See also Arts. 8.6 to 8.8.