BEAM SOLVER CORE - ANALYSIS MANUAL

Introduction

TBD…

Sign Convention

All details below have been excerpted from a paper by I.C.Jong (link: https://icjong.hosted.uark.edu/docu/09.ijee.paper.pdf)

Forces and Moments

  • A shear force is positive if it acts upward on the left (or downward on the right) face of the beam element (e.g., Va at the left end a, and Vb at the right end b in Fig. 1).
  • At the ends of the beam, a moment is positive if it tends to cause compression in the top fiber of the beam (e.g., Ma at the left end a, and Mb at the right end b in Fig. 1)
  • If not at ends of the beam, a moment is positive if it tends to cause compression in the top fiber of the beam just to the right of the position where it acts (e.g., the concentrated moment K and the uniformly distributed moment with intensity m0 in Fig. 1)
  • A concentrated force or a distributed force applied to the beam is positive if it is directed downward (e.g., the concentrated force P, the linearly distributed force with intensity w0 on the left side and intensity w1 on the right side in Fig. 1, where the distribution becomes uniform if w0 = w1 ).

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Deflections and Slopes

  • A positive slope is a counterclockwise angular displacement (e.g., $\theta$a and $\theta$b in Fig. 2).
  • A positive deflection is an upward linear displacement (e.g., ya and yb in Fig. 2)

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