Curved Beams in Bending
Contents:
1. Introduction
2. Locating Neutral Axis
3. Bending Stress
4. Examples
ME 349 INTERMEDIATE MECHANICS OF MATERIALS
Introduction
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Neutral axis and centroidal axis are not the same.
The neutral axis (points on neutral axis have no bending stress)
is at a distance rn from the center of curvature O.
The distance between neutral axis and centroidal axis is e.
ME 349 INTERMEDIATE MECHANICS OF MATERIALS
Locating the Neutral Axis
Refer to Table 3-4:
ME 349 INTERMEDIATE MECHANICS OF MATERIALS
Locating the Neutral Axis
ME 349 INTERMEDIATE MECHANICS OF MATERIALS
Bending Stress
Bending stress at a point at a distance y from the neutral axis,
σ=
My M (rn − r )
=
eAr
eAr
ME 349 INTERMEDIATE MECHANICS OF MATERIALS
Examples
Example 6.1. A certain cross section in a curved beam carries a
bending moment of 500 lb.ft. Determine the bending stress at inner
and outer points on the cross section. The innermost point on the
beam is at a distance of 8-in from the axis of curvature. The crosssection is circular of diameter 2-in.
Example 6.2. Recalculate the bending stresses if the cross-section is
replaced by a square cross section of equal cross-sectional area. The
innermost points are still 8-in away from the axis of curvature.
ME 349 INTERMEDIATE MECHANICS OF MATERIALS
Examples
Example 6.3. Compare the maximum bending stress in a straight
cantilevered beam of circular cross-section of diameter 2-in and
length 8-in carrying a 1 kip load as shown to that of a curved beam of
the same cross-section, curved so as to form a quarter arc subject to
the same load.