CIVIL ENGINEERING FORMULAS

240 CHAPTER NINE

Beams The optimal section modulus for an elastically designed I-shaped beam
results when the area of both flanges equals half the total cross-sectional area of
the member. Assume now two members made of steels having different yield
points and designed to carry the same bending moment, each beam being
laterally braced and proportioned for optimal section modulus. Their relative
weightW 2 /W 1 and relative cost C 2 /C 1 are influenced by the web depth-to-
thickness ratio d/t. For example, if the two members have the same d/tvalues,
such as a maximum value imposed by the manufacturing process for rolled
beams, the relationships are

(9.107)

(9.108)

If each of the two members has the maximum d/tvalue that precludes elastic
web buckling, a condition of interest in designing fabricated plate girders, the
relationships are

(9.109)

(9.110)

Relative steel costs and weights are given in engineering handbooks.* In making
these calculations, the designer must remember that members with the same bend-
ing moment must be compared. Further, the relative costs of girders used for long
spans, may be considerably different from those for conventional structural steel.

Columns For columns, the relative material cost for two columns of different
steels carrying the same load^1 is:

(9.111)

whereFc 1 andFc 2 are the column buckling stresses for the two members. Rela-
tive costs for various structural steels are given in Brockenbrough and Merritt,
Structural Steel Designer’s Handbook, McGraw-Hill.

STEEL CARBON CONTENT AND WELDABILITY

The chemical composition of steel and its welability are often expressed in
terms of the carbon equivalentof the structural steel, given by*

C 2

C 1



Fc 1

Fc 2

p 2

p 1



Fc 1 /p 1

Fc 2 /p 2

C 2

C 1



p 2

p 1 

Fy 1

Fy 2 

1/2

W 2

W 1



Fy 1

Fy 2 

1/2

C 2

C 1



p 2

p 1 

Fy 1

Fy 2 

2/3

W 2

W 1



Fy 1

Fy 2 

2/3

*Brockenbrough and Merritt, Structural Steel Designer’s Handbook, McGraw-Hill.