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In the notes , I dont understand that flange is thin , and the top and bottom surface are free of stress , can someone help to explain please?

Secondly , why the q' is assumed to be q ' throughout the flange is assumed to be 0 ? why are they stress free ? We could see that , the shear force V is applied to the top of the beam right ? enter image description here

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If you are at the face of an element, there cannot be any internal shear stress, because there is nothing to balance it out. The bottom horizontal force I added cannot be balanced by another force since there is no more material at the face of the flange. The thinner your element, the less it will resist in shear and more it will resist in bending. enter image description here

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  • $\begingroup$ Why there is nothing to balance out ? $\endgroup$ – kelvinmacks Nov 18 '16 at 15:48
  • $\begingroup$ To understand what I am saying, you need some basic understanding of free body diagrams (a diagram of an isolated part of your system with all of the loads acting on it). For a free body diagram to be in equilibrium (without acceleration), you need to have all forces in both X and Y directions = 0 and all moments = 0. See my added picture. $\endgroup$ – user2817017 Nov 18 '16 at 22:04
  • $\begingroup$ why The thinner your element, the less it will resist in shear and more it will resist in bending. ? $\endgroup$ – kelvinmacks Nov 28 '16 at 0:03
  • $\begingroup$ Long slender elements will resist deformation in bending simply because their bending stiffness is higher than their shear stiffness. See attached pdf : files.engineering.com/… $\endgroup$ – user2817017 Nov 30 '16 at 2:33
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If you recall from practicing finding Vy when you make cuts along a beam, you have a shear force (Vy) on each side of the cut, each opposite and equal to the other. Now imagine cutting nothing off the surface of a body. What is the shear force of the surface? Nothing! Why? Because the shear force of the nothing you cut off is...nothing. Equal and opposite, remember?

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