This result for pure, one-way bending can, by superposition, be used to gen-erate the solution for combined bending of prismatic beams where a moment, My , is applied in addition to Mz.

**Pure Bending of
Plates **

This result for pure,
one-way bending can, by superposition, be used to gen-erate the solution for
combined bending of prismatic beams where a moment, *M _{y}* , is
applied in addition to

First consider a plate of uniform thickness, *h*,
in pure bending around only the *y* axis due to a uniformly distributed
moment, *M _{y}* , per unit length. The top and bottom of the plate
will become anticlastic surfaces as shown in Figure 5.7 with the curvature 1/ρ convex in the

With distributed moments along both perpendicular
edges (Figure 5.7c), the curvatures, stresses, and deflections can be found by
superposition. With a bending moment per unit length around the *x* axis, *M _{x}*,
as well as

and the corresponding stresses are σ_{i =}*M _{i}z*/

The assumption of an anticlastic surface corresponds
to the assumption that the vertical deflection is very small in comparison to
the thickness. For this situation, we can use the approximation that the
curvatures are given by the second derivatives of the deflection:

Two special cases are of particular note. To bend
the plate into a cylindrical sur face, say one with the longitudinal direction
parallel to the *y* axis

Usually the moments in plates are not constant, even
away from the boundaries due to surface loads that introduce shears. However,
just as for beams, these formulas for pure bending can be used with confidence
away from stress-concentration points if the thickness is small compared to the
width and length of the plate.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

Civil : Principles of Solid Mechanics : Linear Free Fields : Pure Bending of Plates |

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