CIVIL ENGINEERING FORMULAS

84 CHAPTER THREE

If, as in certain classes of masonry construction, the material cannot withstand
tensile stressand, thus, no tension can occur, the center of moments (Fig. 3.3) is
taken at the center of stress. For a rectangular section,Pacts at distance kfrom the
nearest edge. Length undercompression 3 k, and SM^2 / 3 P/hk. For a circular

section,SM[0.372 0.056 (k/r)]P/k ,whererradius and kdistance
ofPfrom circumference. For a circular ring,Saverage compressive stress on
cross section produced by P;eeccentricity of P;zlength of diameter under
compression (Fig. 3.4). Values of z/rand of the ratio of Smaxto average Sare given
in Tables 3.3 and 3.4.

rk

TABLE 3.2 Typical Short-Column Formulas

Formula Material Code Slenderness ratio

Carbon steels AISC

Carbon steels Chicago

Carbon steels AREA

Carbon steels Am. Br. Co.

Alloy-steel ANC

tubing

Cast iron NYC

2017ST ANC

aluminum

Spruce ANC

Steels Johnson

Steels Secant

*Scrtheoretical maximum; cend fixity coefficient; c2, both ends pivoted; c2.86, one

pivoted, other fixed; c4, both ends fixed; c1 one fixed, one free.

†Is initial eccentricity at which load is applied to center of column cross section.

l

r

†Scr critical

Sy

1 

ec

r^2

sec 

l

rB

P

4 AE

l

r



B

2 n 

2 E

Sy

*ScrSy 1 

Sy

4 n 

2 E

l

r

2



1

wcr

*Scr5,000  72

0.5

c 

l

r

2

1

wcr

*Scr34,500  94

245

wc 

l

r

l

r

Sw9,000 (^40)   70
l
r
l
wcr
*Scr135,000  65
15.9
c 
l
r
2
60 
l
r
Sw19,000 (^100)   120
l
r
l
r
Sw15,000 (^50)   150
l
r
l
r
Sw16,000 (^70)   120
l
r
l
r
Sw17,0000.485  120
l
r
2