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Presentation on SFD- Shear Force Diagram

WELCOMETOMY Presentation onSFD- Shear Force DiagramBy-Enamul Nasir10.01.03.1334th Year 2nd SemesterDept. Of Civil EngineeringAhsanullah University Of Science and Technology

What is SHEAR FORCE?Shear force: is the algebraic sum of the vertical forces acting to the left or right of a cut section along the span of the beam.What is SHEAR FORCE DIAGRAM?Shear force diagram(SFD): The graphical representation of shear force in which ordinates represents shear force and the abscissa represents the position of the section is called shear force diagram or it can be defined as A shear force diagram is the one which shows the variation shear force along the length of a beam section.

What is the importance of SFD in case of designing structures?Shear force diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear force at a given point of a structural element such as a beam. These diagrams can be used to easily determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure. Sign convention for SFD drawing? The normal convention used in most engineering applications is to label a positive shear force one that spins an element clockwise (up on the left, and down on the right).

Also for simplification in solving many structural problems the shear force at a section will be considered positive when the resultant of the forces to the left section is upwards, or to the right of the section is downward.

IMPORTANT POINTS FOR DRAWING SHEAR FORCE DIAGRAMConsider the left or right portion of the section,

Add the forces ( including reactions ) normal to the beam on one of the portion. [ If right portion of the section is chosen, a force on the right portion acting downwards is positive while a force acting upward is negative, if left section is chosen then sign convention will be vice versa. ]

The positive values of shear force are plotted above base line, and negative values below base line.

The shear force diagram will increase or decrease suddenly by a vertical straight line at a section where there is a vertical point load.The shear force between any two vertical loads will be constant and hence the shear force diagram between any two vertical loads will be horizontal.

WHAT IS THE USE OF SFD? To determine the internal shear forces at any given point on a rigid body.

PRACTICAL APPLICATION OF SHEAR FORCE DIAGRAMThe figure below is referring the practical application of shear force diagram in case of designing shear reinforcement of a beam.

Some Examples of SFDSimply Supported beam with UDL

Simply supported beams with triangular load

Cantilever Beam

Cantilever beam carrying Three Loads

Simply Supported beam carrying double point load and UDL

A detail example of drawing SHEAR FORCE DIAGRAMA simply supported beam overhanging on one side is subjected to a U.D.L. of 1 kN/m. Sketch the shear force diagram.Solution: Consider a section (X X) at a distance x from end C of the beam.

To draw the Shear Force Diagram, RA and RB has to be defined,

By taking moment of all the forces about point AMA =0RB 3 w/2 (4)2 = 0 RB = 1 (4)2 / 2 3 = 8/3 kN

For static equilibrium;Fy = 0RA + RB 1 4 = 0 RA = 4 8/3 = 4/3 kN

Now, To draw SFD we need S.F. at all salient points:Taking a section between C and B, SF at a distance x from end C. we have,

Fx = + w.x kN At x = 0; FC = 0 x = 1 m; FB just right = 1 1 = + 1 kN Now, again taking section between B and A, at a distance x from end C, the SF is:

Fx = x 8/3When, x = 1 m; FB = 1 8/3 = 5/3 kN = 1.67 kN At x = 4 m; FA = 4 8/3 = + 4/3 kN = + 1.33 kN

When The S.F. becomes zero;Fx = x 8/3 = 0 x = 2.67 m

(The sign is taken positive taken when the resultant force is in downward direction on the RHS of the section).

Now the Final Shear Force Diagram

The SFD can be drawn by joining the ordinates at salient point by straight line, as defined by governing equations.

NECESSITY OF SFD IN CASE OF PRESTRESSED CONCRETEPrestressed-concrete beams possess greater reliability in shear resistance than reinforced-concrete beams, because prestressing will usually prevent the occurrence of shrinkage cracks which could conceivably destroy the shear resistance of the reinforced-concrete beams, especially near the point of contra flexure. Since so many prestressed-concrete beams have been designed and built on the basis of assumed theories for shear resistance, and since beams are not falling in shear, it may be concluded that the present method of design is a safe one. As result it can be said that the necessity of SFD in case of prestressed-concrete is not too much important.THANK YOUALL