Shear Force and Bending Moment Diagrams [SFD.pdf

BEAMS AND SHEAR FORCE & BENDING MOMENT DIAGRAMS. Presented By: G.Suresh M.Tech NIT-Tiruchirappalli

Topics Covered  What is Beam? What are main types of Beams?  What are the types of loads applied on to beams?  What is SFD and BMD? It’s Importance.

 How to draw SFD and BMD?

What is Beam and types of beams  Beam is a structural member of a system having external loading at right angles to it’s axis.

Types of beams  According to end supports:

 According to cross section:

 According to Equilibrium condition: Statistically determinate and statistically Indeterminate  According to geometry: Straight Beam, Curved Beams and Tapered Beams.

Types of loading on Beams 1. Concentrated or Point load 2. Uniformly distributed load( UDL) 3. Uniformly varying load (UVL) •

Triangular loads

•

Trapezoidal loads

Analysing the Shear Force and Bending Moment  Shear Force: Shear force is the vertical force  Moment: It is the product of force and perpendicular distance between line of action in the bead acting perpendicular to it’s axis. Shear Force Diagram (SFD): The diagram which shows the variation of shear force along the length of the beam is called Shear Force Diagram (SFD)

 Bending Moment (BM): The moment which causes the bending effect on the beam is called Bending Moment. It is generally denoted by ‘M’ or ‘BM’. Bending Moment Diagram (BMD): The diagram which shows the variation of bending moment along the length of the beam is called Bending Moment Diagram (BMD).

 force and the point about which moment is required to be calculated.

Sign convection of SF and BM Shear Force:

F F

 Bending moment: It’s considers as sagging and hogging depends upon the curvature of convexvity.

F F + ve shear force

Sagging

Hogging

- ve shear force

“Happy” Beam is +VE

C o n

“Sad” Beam is -VE

Relationship between Load, Shear Force and Bending moment

dM v dx dv w dx Type of load SFD/BMD Shear Force Diagram Bending Moment Diagram

It is the relation between shear force and BM It is the relation between intensity of Load and shear force Between point loads OR Uniformly distributed for no load region load Horizontal line

Inclined line

Inclined line

Two-degree curve (Parabola)

Uniformly varying load

Two-degree curve (Parabola) Three-degree curve (Cubic-parabola)

Points to be Remembered  Point of Contra flexure (POC): It’s the point at which bending moment changes it’s sign or the curvature of beam reverse it’s direction.  Point of inflection(POI):

It’s the point at which the bending moment is zero. Note: All POC’s are POI’s but all POI’s are need not be POC’s. Note: there can be more than 1 point of contra flexure in Bending moment diagram

SDF and BMD for Simply Supported Beam

SDF and BMD for Cantilever Beam.

Example Problem 1 1.Draw shear force and bending moment diagrams [SFD and BMD] for a simply supported beam subjected to three point loads as shown in the Fig. given below.