"CESE 656 – Advanced Mechanicsfor Structural EngineersCivil Structural EngineeringUniversity of Alabama at BirminghamShear Center Shear CenterLocation of loading that causes bending without twisting2 Shear Center CESE 656 Shear Loading Not Along an Axis of Symmetry? Consider the channel section loaded through its centroidas shown? This loading causes the channel to deflect downward andto twist? Why?3 Shear Center CESE 656 Shear Loading Not Along an Axis of Symmetry? Examine shear flow along section A-A‘? Shear flow in web is up (in the direction of V)? Shear in top flange flows away from web? Shear in bottom flange flows toward web? The flange shear flows create a torque about the section centroid that isnot balanced by the applied load? The beam twists in response to this torque4 Shear Center CESE 656 Concept of Shear Center? Shear Center – The point where transverse load isapplied that results in no twisting of the cross-section? Consider the channel again? The shearing forces in the flanges create a CCW torque onthe cross-section? If the load P is moved to the right, it creates a CW torque onthe cross-section? The shear center is located sothat these torques are balanced? Shear Center is a property only of the cross-section geometry5 Shear Center CESE 656 Shear Center? When a transverse load is applied through the shearcenter, the beam bends without twistingLoaded Through Loaded ThroughCentroid Shear Center6 Shear Center CESE 656 Symmetric Sections? Shear Center is always located along an axis of symmetry? For doubly symmetric sections the shear center coincideswith the centroid7 Shear Center CESE 656 Finding the Shear Center1. Assume the beam cross-section bends without twisting2. Determine the shear flow and the resultant internalshear forces3. Locate the shear center by setting the torque caused bythe internal shear flow equal to the torque caused bythe external shear force8 Shear Center CESE 656 Shear Center for Thin-walledOpen Symmetric Sections9 Shear Center CESE 656 Example – Shear Center for a Channel? Locate the shear center for the channel section shownA? If t is small3 2 2 ? h h h ? h t ? ? w? ? = + 2 ? ? = + ? ?? ? 12 2 2 6 h ? ? ? ? ? ? ? ? ? ? 2 ? ? ? ? = = =?? ? ? 2 ? h h ? h ? ? t ? fh + ? ? + ? ? ? ? 6 2 6 2 ? ? ? 1 ? ? ? ? ? = ? ? = =? ?? ? ? ? h ? 2 ? h 2 h + ? ? ? ? 2h + 1 6 6 ? ? ? 10 Shear Center CESE 656 "