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# Shear Stress; Id no.: 10.01.03.033

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### Shear Stress; Id no.: 10.01.03.033

1. 1. CE 416 Prestress Concrete Design Sessional Course Teacher Ms. Sabreena Nasrin Mr. Galib Muktadir Ratul Department of Civil Engineering
2. 2. Definition Shear Force vs Shear Stress Shear Stress on Beam Sign Convention Mohr Circle Shear Stress in Steel Calculating Shear Stress Horizontal and Vertical Shear Stress Shear Stress in Concrete Other Form of Shear Stress Testing Machine of Shear Stress Shear Stress Distribution
3. 3.  A shear stress, denoted (Greek: tau), is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section.  It is the form of stress that subjects an object to which force is applied to skew, tending to cause shear strain.
4. 4. Shear Stress Parallel to the Cross Section (Horizontal) Shear Stress in 2D View Shear Stress Parallel to the Cross Section (Inclined) Shear Stress in 3D View
5. 5. A shear stress between two objects occurs when a force pulls the object along the same plane as the face of the object abutting another object that is being pulled in the opposite direction. A shear stress within an object will occur when a force parallel to the plane causes one plane of the material to want to slip against another, thus deforming the material.
6. 6.  If a fluid is placed between two parallel plates spaced 1.0 cm apart, and a force of 1.0 dyne is applied to each square centimeter of the surface of the upper plate to keep it in motion, the shear stress in the fluid is 1 dyne/cm2 at any point between the two plates.  The formula to calculate average shear stress is: where: = the shear stress; = the force applied; = the cross-sectional area of material with area parallel to the applied force vector.
7. 7. Measure the area, say value A, of the material over which the force is applied. The area of a simple rectangular or squareshaped cross section is obtained by multiplying the length by the height. The area of a circular cross section is calculated by the equation A= pi*r^2. The area of a circle is equal to the value of pi (3.14159) multiplied by the squared radius of the circle. Measure the force that is to be applied over the area, say value F. Simple forces of weight can be measured with a scale that displays results in pounds. Substitute the values obtained in the above steps as the following formula: T=F/A; where T = the shear stress, F = the force applied and A = the cross-sectional area over which the force was applied at first. Divide the numerical value for F by the value for A and the resulting number is the calculated shear stress.
8. 8. It is the shear component of an applied tensile (or compressive) stress resolved along a slip plane that is other than perpendicular or parallel to the stress axis. τ = σ cos Φ cos λ It is the value of resolved shear stress at which yielding begins; it is a property of the material. τ =σ (cosΦ cosλ)max
9. 9. It is the stress on the mechanical elements of that surface - something like the stress in a bolt that is connecting two pieces of metal. If the bolt cracks straight across, if failed due to the shear. It is the stress when something lands on a surface - something like when a person falls off a bike and skids across the ground. The shear stress tears their skin.
10. 10. Some Shear Testing Machines
11. 11. Transverse Shear Force: ΣF = 0 (V = RA in this case) Transverse Shear Stress: fv = V/A
12. 12. The circle is centered at the average stress value, and has a radius R equal to the maximum shear stress, as shown in the figure. The maximum shear stress is equal to one-half the difference between the two principal stresses,
13. 13. Ɵs is an important angle where the maximum shear stress occurs. The shear stress equals the maximum shear stress when the stress element is rotated 45 away from the principal directions. The transformation to the maximum shear stress direction can be illustrated as:
14. 14. Horizontal & Vertical Shear Stress
15. 15. Let us begin by examining a beam of rectangular cross section. We can reasonably assume that the shear stresses τ act parallel to the shear force V. Let us also assume that the distribution of shear stresses is uniform across the width of the beam.
16. 16. 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.
17. 17. 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. Shown below is a rectangular beam in pure bending.
18. 18. Let Q = First moment of area =∫ydA τ =VQ/Ib Where: V = transverse shear force Q = first moment of area (section above area of interest) I = moment of inertia b = width of section For the rectangular section shown above: τ =V/2I(h² /4) – y1²) As shown above, shear stresses vary quadratic ally with the distance y1 from the neutral axis. The maximum shear stress occurs at the neutral axis and is zero at both the top and bottom surface of the beam.
19. 19. For a rectangular cross section, the maximum shear stress is obtained as follows: Q = (bh/2)(h/4) = bh²/8 I = bh²/12 Substituting yields: Ʈmax = 3V/2A For a circular cross section: Ʈmax = 4V/3A
20. 20. Steel is affected by the compression component of Shear. In case of tension there is no problem. Problem: Web Crippling Solution: Web Stiffeners
21. 21. Concrete is affected by the tensile component of principal shear stress. In case of compression there is no problem. Problem: Diagonal Cracking Solution: Shear Reinforcement
22. 22. Shear Stress Distribution in a Rectangular Section Shear Stress Distribution in a Triangular Section
23. 23. Shear Stress Distribution in a Wide Flange Section
24. 24. Shear Stress Distribution in a Circular Section Shear Stress Distribution in a T Section
25. 25. Thank you all… 