CIVIL ENGINEERING FORMULAS

70 CHAPTER TWO

TABLE 2.6 Crescent-Beam Position Stress Factors (see Fig. 2.23)*

Angle ,

k

degree Inner Outer

10 1 0.055H/h 1 0.03H/h

20 1 0.164H/h 1 0.10H/h

30 1 0.365H/h 1 0.25H/h

40 1 0.567H/h 1 0.467H/h

50 1 0.733H/h

60 1 1.123H/h

70 1 1.70H/h

80 1 2.383H/h

90 1 3.933H/h

*Note: All formulas are valid for 0 H/h0.325. Formulas for the inner boundary,

except for 40 degrees, may be used to H/h0.36.Hdistance between centers.

2.531

(0.29390.7084H/h)1/2

0.3542

2.070

(0.48171.298H/h)1/2

0.6492

1.756

(0.24160.6506H/h)1/2

0.6506

1.521

(0.51711.382H/h)1/2

1.382

FIGURE 2.24 (a) Simple beam subjected to equal end moments. (b)

Elastic lateral buckling of the beam.

M

Compressive stress

Tensile stress

L

(a)

β

Mcr

Mcr

(b)

M