Page 130 - Civil Engineering Formulas

72 CHAPTER TWO

moment, M cr may be obtained by multiplying M cr given by the previous equa-
tions by an amplification factor

M cr C b M cr (2.28)
12.5M max
where C b (2.29)
2.5M max 3M A 4M B 3M C
and M max absolute value of maximum moment in the unbraced beam segment
M A absolute value of moment at quarter point of the unbraced beam
segment
M B absolute value of moment at centerline of the unbraced beam segment
M C absolute value of moment at three-quarter point of the unbraced
beam segment
C b equals 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 superposition if 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.
2
The maximum stress, lb/in (MPa), equals
P Mc
f (2.30)
A I

where P axial load, lb (N)
2
2
A cross-sectional area, in (mm )
M maximum bending moment, in lb (Nm)
c distance from neutral axis to outermost fiber at the section where max-
imum moment occurs, in (mm)
4
4
I moment of inertia about neutral axis at that section, in (mm )
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
P c
f (M Pd) (2.31)
A I
where d is 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