Building Design and Construction Handbook - Merritt - Ventech!

FIGURE 5.32 Concentrated load at any point
of a simple beam.
STRUCTURAL THEORY 5.47
FIGURE 5.33 Concentrated load at midspan
of a simple beam.
stress is the sum of the stress due to this moment and the stress due to P applied
as an axial load:
� �
P Pec P ec
ƒ � � � 1 � (5.70)
2
A I A r
where A � cross-sectional area
c � distance from neutral axis to outermost fiber
I � moment of inertia of cross section about neutral axis
r � radius of gyration, which is equal to �I/A
Figure 5.26 gives values of the radius of gyration for some commonly used cross
sections.
For an axial compression load, if there is to be no tension on the cross section,
e should not exceed r 2 /c. For a rectangular section with width b and depth d, the
eccentricity, therefore, should be less than b/6 and d/6; i.e., the load should not
be applied outside the middle third. For a circular cross section with diameter D,
the eccentricity should not exceed D/8.
When the eccentric longitudinal load produces a deflection too large to be neglected
in computing the bending stress, account must be taken of the additional
bending moment Pd, where d is the deflection. This deflection may be computed
by employing Eq. (5.62) or closely approximated by