enter image description hereI need help with this problem. Suppose we have a cantilever with width $-c \leq y \leq c$ and length $x=l$ fixed at $x=0$. We know that it is loaded by uniform shear along the lower edge with magnitude $S$ and the upper edge and the end $x=l$ are free from load. I know how to find the stresses using the airy stress function, but could you please tell me how to find $\sigma_x$ and $\tau_{xy}$ using the elementary tension and bending formula so that I can compare?

The depth of the beam perpendicular to the x axis is 1.

  • $\begingroup$ Can you provide picture? $\endgroup$ – Jem Eripol Sep 27 '17 at 23:56
  • $\begingroup$ What is the width of the beam perpendicular to the x-axis? $\endgroup$ – Jem Eripol Sep 28 '17 at 3:05
  • $\begingroup$ @JemEripol assume it is 1. $\endgroup$ – David Sep 28 '17 at 11:13
  • $\begingroup$ elementary Euler beam theory does not directly handle the surface shear case. You might replace "s" with an axial force and a distributed moment, although without actually going through all the math its not clear how good an approximation that would yield. $\endgroup$ – agentp Sep 29 '17 at 15:00

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