Department Of Civil Engineering
Name: Pias Chakraborty
4th Year 2nd Semester
• Course No.
: CE 416
• Course Title
: Pre-stressed Concrete Lab.
• Course Teacher : Sabreena Nasrin Madam &
Munshi Galib Muktadir Sir
Topic Of Presentation: Shear Stress
• In solid mechanics, stress is defined as force
divided by cross sectional area, i.e. stress =
force/area. Stress is generally two types.
• The shear stress (τ) acts parallel to the selected plane
& determined by τ = F / .
• Figure shows a rod where forces applied parallel to the
rod’s cross sectional area. The stress here is defined as
• Pure Shear- Pure shear stress is related to pure shear
strain(ɤ) & denoted by τ =ɤG, 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. τ= VQ/IB.
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
• By finding the angle between force and sectional
area, i.e. whether this is zero, 90 or something in
between them. When θ = 0 there is only shear
stress, for θ = 90 we just have normal stress and
for θ = 45 we have both shear and normal
• Shear stress can cause deformation. Figure
shows the shear stress and its deformation on
a plane. This plane is subjected to the shear
stress τ. Shear stress acts tangential to the
surface of material element. It observed to
deform into a parallelogram.
• 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.
• 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 τ act parallel to
the shear force V.
• 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.
• The existence of horizontal shear stresses in a
beam can be demonstrated as follows.
• A single bar of depth 2h is much stiffer that
two separate bars each of depth h.