3. In solid mechanics, stress is defined as force
divided by cross sectional area, i.e.
stress=force/area.
Stress is generally two types.
Stress
4. • The shear stress (ꚍ) acts parallel to the selected plane
& determined by ꚍ=F/A.
• Figure shows a rod where forces applied parallel to the
rod’s cross sectional area. The stress here is defined as
shear stress.
6. • Pure shear- pure shear stress is related to pure shear
strain (ᵧ) & denoted by ꚍ=G , G=shear modulus.
• Beam shear- beam shear is defined as the internal
shear stress of a beam caused by the shear force
applied to the beam, i.e.
• Where V= total shear force at the location in question;
Q= statical moment of area;
• B= thickness in the material perpendicular to the shear;
• I=moment of Inertia of the entire cross sectional area.
7. • By finding the angle between force and sectional
area, i.e. whether this is zero, 90 or something in
between them. When angle=0 there is only shear
stress, for angle=90 we just have normal stress and
for angle=45 we have both shear and normal stress.
•
8. • Shear stress can cause deformation. Figure shows
the shear stress and its deformation on a plane. This
plane is subjected to the shear stress . Shear stress
acts tangential to the surface of material element. It
observed to deform into a parallelogram.
9. • Shear stresses are usually maximum at the
neutral axis of a beam (always if the thickness
is constant or if thickness at neutral axis is
minimum for the cross section, such as for I-
beam or T-beam), but zero at the top and
bottom of the cross section as normal stresses
are max/min.
10. • When a beam is subjected to a loading, both bending
moments, M, and shear forces, V, act on the cross
section. Let us consider a beam of rectangular cross
section. We can reasonably assume that the shear
stresses act parallel to the shear force V.
11. • Shear stresses on one side of an element are
accompanied by shear stresses of equal magnitude
acting on perpendicular faces of an element. Thus,
there will be horizontal shear stresses between
horizontal layers (fibers) of the beam, as well as ,
transverse shear stresses on the vertical cross
section. At any point within the beam these
complementary shear stresses are equal in
magnitude.
12. • The existence of horizontal shear stresses beam can
be demonstrated as follows.
• A single bar of depth 2h is much stiffer that two
separate bars each of depth h.
