Shear centre

Concept of Shear centre with example

1. SHEAR CENTRE PRESENTED BY: Aiswarya Ray-B120100ME Anirudh Ashok-B120325ME Mahesh M.S.- Harikumar Ashish Ranjan Deepesh

2. NEED FOR FINDING LOCATION OF SHEAR CENTRE In unsymmetrical sections, if the external applied forces act through the centroid of the section, then  in addition  to bending, twisting is also produced. To avoid twisting, and cause only bending, it is necessary for the forces to act through the particular point, which may not coincide with the centroid . The position of the this point is a function only of the geometry of the beam section. It is termed as  shear center.

3. WHAT IS SHEAR CENTRE?? Shear center is defined as the point on the beam section where load is applied and no twisting is produced . - At shear center, resultant of internal forces passes . - On symmetrical sections, shear center is the center of gravity of that section . - Such sections in which there is a sliding problem, we place loads at the shear center.

4. 4 PROPERTIES OF SHEAR CENTRE The shear center lays on the axis of symmetry. Thus for twice symmetrical section the shear centre is the point of symmetry axes intersection. If the cross section is composed of segments converging in a single point, this point is the shear centre. The transverse force applied at the shear centre does not lead to the torsion in thin walled-beam. The shear centre is the centre of rotation for a section of thin walled beam subjected to pure shear. The shear center is a position of shear flows resultant force, if the thin-walled beam is subjected to pure shear.

5. DETERMINING LOCATION OF SHEAR CENTRE

6. Now for Force equilibrium in x-direction, ∆x - ∫ s tds + ∫ s (σ x + ∆x) tds = 0   SHEAR STRESSES IN THIN-WALLED OPEN SECTIONS Consider a beam having a thin-walled open section as shown above. Now consider an element of length ∆x at section x as shown.

7. ie. = – ∫ s tds t s → wall thickness at s Observing M y = 0, normal stress, σ x is given by σ x = M z Hence, = Recalling from strength of materials that = – V y , and substituting We get, ]      

8. 1 st moments of area about the z and y-axis respectively Since for shear centre twisting caused is zero, The moment due to shear stress = The moment due to the load applied Moment of about centroid  

9. Shear Centre in Real Life Situations

10. Purlins Construction of Purlins   A purlin is any longitudinal, horizontal, structural member in a  roof .  

11. The point of application of load is important , depending on the cross-section of purlin .

12. If an unsupported channel section is loaded closer to its shear centre, it'll take more load before buckling than if you put the load over the centre of the channel, the application being that you can get more load out of the same member. Useful in design of thin walled open steel sections as they are weak in resisting torsion. 

13. SHEAR CENTRE PROBLEM A beam has the cross section composed of thin rectangles as shown in fig. The loads on the beam lie in a plane perpendicular to the axis of symmetry of cross section and so located that the beam does not twist .Bending load cause for any section a vertical shear V. determine the location of shear center.

14. Q. (a) Locate the shear center S of the hat section by determining the eccentricity, e. (b) If a vertical shear V =10 kips acts through the shear center of this hat what are the values of the shear stresses τ A at the location and direction indicated in Figure.

15. Solution : The centroidal principal moment of inertia of the beam section is

16. The first moment areas of the locations shown in figure are

17. The shear stresses at these locations are τ A = 2618 psi

18. The moment about point A is the resultant forces are