CIVIL ENGINEERING FORMULAS

BEAM FORMULAS 69

TABLE 2.5 Stress Factors for Inner Boundary at Central Section (see Fig. 2.23)

1.For the arch-type beams

(a)

(b)

(c)In the case of larger section ratios use the equivalent beam solution

2.For the crescent I-type beams

(a)

(b)

(c)

3.For the crescent II-type beams

(a)

(b)

(c)K1.081

h

RoRi

0.0270

if

RoRi

h

    20

K1.119

h

RoRi

0.0378

if 8 

RoRi

h

 20

K0.8971.098

h

RoRi

if

RoRi

h

 8

K1.092

h

RoRi

0.0298

if

RoRi

h

    20

K0.9590.769

h

RoRi

if 2 

RoRi

h

 20

K0.5701.536

h

RoRi

if

RoRi

h

 2

K0.8991.181

h

RoRi

if 5 

RoRi

h

 10

K0.8341.504

h

RoRi

if

RoRi

h

 5

section determined above must then be multiplied by the positi on factor k,
given in Table 2.6. As in the concentric beam, the neutral surfaceshifts
slightly toward the inner boundary. (See Vidosic, “Curved Beams with Eccen-
tric Boundaries,” Transactions of the ASME, 79 , pp. 1317–1321.)

ELASTIC LATERAL BUCKLING OF BEAMS

When lateral buckling of a beam occurs, the beam undergoes a combination of
twist and out-of-plane bending (Fig. 2.24). For a simply supported beam of
rectangular cross section subjected to uniform bending, buckling occurs at the
critical bending moment, given by

Mcr (2.26)

L^2

EIyGJ