Department Of Civil Engineering

Name: Pias Chakraborty4th Year 2nd Semester

ID: 10.01.03.139

• Course No. : CE 416• Course Title : Pre-stressed Concrete Lab.• Course Teacher : Sabreena Nasrin Madam & Munshi Galib Muktadir Sir

Topic Of Presentation: Shear Stress

What Is Stress?

• In solid mechanics, stress is defined as force divided by cross sectional area, i.e. stress = force/area. Stress is generally two types.

STRESS

NORMAL STRESS

SHEAR STRESS

What Is General Shear Stress?

• The shear stress (τ) acts parallel to the selected plane & determined by τ = 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.

Shearing Stresses In Bolts

Other Forms of Shear Stresses

• 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 area.

Identifying Shear Stress Over Normal• 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 stresses.

Result Caused By Shear Stress• 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 In Beams • 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.

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