Handbook of Civil Engineering Calculations

/= (1/12)(0.25)(8.44)

3

• 12.52 in
  4
  (521.121 cm
  4
  ) > 3.42 in
  4
  (142.351 cm
  4
  ). This is ac-
  ceptable.
  The stiffeners must be in intimate contact with the compression flange, but they may
  terminate I^3 A in (44.45 mm) from the tension flange. The connection of the stiffeners to
  the web must transmit the vertical shear specified in the Specification.

13. Design the bearing stiffeners at the supports
    Use the directions given in the Specification. The stiffeners are considered to act in con-
    junction with the tributary portion of the web to form a column section, as shown in Fig.


14. Thus, area of web = 5.25(0.438) = 2.30 in^2 (14.839 cm^2 ). Assume an allowable stress of
    20 kips/in^2 (137.9 MPa). Then, plate area required = 207/20 - 2.30 = 8.05 in^2 (51.938
    cm^2 ).
    Try two plates 10 x Y 2 in (254.0 x 12.7
    mm), and compute the column capacity of the
    section. Thus, A = 2(10)(0.5) + 2.30 = 12.30
    in^2 (79.359 cm^2 ); /= (1/12)(0.5)(20.44)^3 - 356
    in^4 (1.4818 dm^4 ); r = (356/12.30)°^5 - 5.38 in
    (136.652 mm); LIr = 0.75(68)/5.38 = 9.5.
    Enter the table of slenderness ratio and al-
    lowable stress in the Manual with the slender-
    ness ratio of 9.5, and obtain an allowable stress
    of 21.2 kips/in
    2
    (146.17 MPa). Then / -
    207/12.30 = 16.8 kips/in
    2
    (115.84 MPa) < 21.2
    kips/in^2 (146.17 MPa). This is acceptable.
    Compute the bearing stress in the stiffeners pIGURE 9 Effective column ^n
    In computing the bearing area, assume that
    each stiffener will he clipped 1 in (25.4 mm) to
    clear the flange-to-web welding. Then / =
    207/[2(9)(0.5)] = 23 kips/in^2 (158.6 MPa). The
    Specification provides an allowable stress of
    33 kips/in
    2
    (227.5 MPa).
    The 10x1/2 in (254.0 )( 12.7 mm) stiffeners at the supports are therefore satisfactory
    with respect to both column action and bearing.

Steel Columns and Tension Members

The general remarks appearing at the opening of the previous part apply to this part as
well.
A column is a compression member having a length that is very large in relation to its
lateral dimensions. The effective length of a column is the distance between adjacent
points of contraflexure in the buckled column or in the imaginary extension of the buck-
led column, as shown in Fig. 10. The column length is denoted by L, and the effective
length by KL. Recommended design values of K are given in the AISC Manual.
The capacity of a column is a function of its effective length and the properties of its
cross section. It therefore becomes necessary to formulate certain principles pertaining to
the properties of an area.
Consider that the moment of inertia / of an area is evaluated with respect to a group of
concurrent axes. There is a distinct value of/associated with each axis, as given by earli-

stiffener plate

web plate