2. BENDING STRESSES IN BEAMS 3. When a beam length is subjected
to a constant amount ofbending moment & a zero shear force ,
the stresses set upacross the cross-section of the beam , due to
bending isknown as PURE BENDING STRESS. 4. Due to bending of beam ,
layer which is neithercompressed nor stretched , is known as
NEUTRALLAYER. 5. The line of intersection of neutral layer , with
anynormal cross-section of a beam is known asNEUTRAL AXIS of that
section. 6. When a beam length is subjected to a constant amount
ofbending moment, on one side of neutral axis there arecompressive
stresses and on the other there are tensile stresses .These
stresses form a couple, whose moment must be equal toexternal
moment M.The moment of this couple, which resists the external
bendingmoment , is known as MOMENT OF RESISTANCE. 7. Assumptions in
the theory of PUREBENDING:-i. The material of the beam is perfectly
homogeneousand isotropic.ii. The beam is stressed within its
elastic limit andHooks law (stress is preposanal to stress) is
valid.iii. The transverse sections, which were plane beforebending
remain plane after bending.iv. Each layer of beam is free to expand
or contract,independently.v. The value of youngs modulus (E) is the
same intension & compression. 8. Flexure equation :- 9. Where ,
M=Moment of resistanceI=Moment of Inertia of the section about x-x
axisf=Bending stress(maximum)y=Distance of extreme fiber from
neutral axisE=Modulus of elasticityR=Radius of curvature of the
beam 10. Moment of resistance(M) for somesimple beams 11.
Cantilever beam with U.D.L:M=wl/2 12. Cantilever beam with point
load:M=w.l 13. Simply supported beam with U.D.L:M=wl/8 14. Simply
supported beam witheccentric point load:M=Wab/l 15. Simply
supported beam withcentral point load:M=Wl/4 16. When a section of
beam is made up of two or more differentmaterials, joined together
,in such a manner that they behavelike a single piece and each
material bends to the same radius ofcurvature. Such a beam is
called FITCHED BEAM. 17. THANK YOU
