CIVIL ENGINEERING FORMULAS

72 CHAPTER TWO

moment,Mcrmay be obtained by multiplying Mcrgiven by the previous equa-

tions by an amplification factor

(2.28)

where (2.29)

andMmaxabsolute value of maximum moment in the unbraced beam segment

MAabsolute value of moment at quarter point of the unbraced beam

segment

MBabsolute value of moment at centerline of the unbraced beam segment

MCabsolute value of moment at three-quarter point of the unbraced

beam segment

Cbequals 1.0 for unbraced cantilevers and for members where the moment

within a significant portion of the unbraced segment is greater than, or equal to,

the larger of the segment end moments.

COMBINED AXIAL AND BENDING LOADS

For short beams, subjected to both transverse and axial loads, the stresses are

given by the principle of superpositionif the deflection due to bending may be

neglected without serious error. That is, the total stress is given with sufficient

accuracy at any section by the sum of the axial stress and the bending stresses.

The maximum stress, lb/in^2 (MPa), equals

(2.30)

wherePaxial load, lb (N)

Across-sectional area, in^2 (mm^2 )

Mmaximum bending moment, in lb (Nm)

cdistance from neutral axis to outermost fiber at the section where max-

imum moment occurs, in (mm)

Imoment of inertia about neutral axis at that section, in^4 (mm^4 )

When the deflection due to bending is large and the axial load produces

bending stresses that cannot be neglected, the maximum stress is given by

(2.31)

wheredis the deflection of the beam. For axial compression, the moment Pd

should be given the same sign as M; and for tension, the opposite sign, but the

f

P

A

(MPd)

c

I

f

P

A



Mc

I

Cb

12.5Mmax

2.5Mmax 3 MA 4 MB 3 MC

McrCbMcr