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(Solved): (60%) A simple beam AB with a T-section supports a concentrated load P acting at distances a and b f ...
(60%) A simple beam AB with a T-section supports a concentrated load P acting
at distances a and b from the left-hand and right-hand supports, respectively (see
Figure 2). The material used in this beam has Young's modulus E and Poisson's
ratio v.
(a) Determine the maximum bending moment M_(max ) and maximum shear force V_(max )
of this beam. Indicate the cross section where the maximum bending moment or
the maximum shear force occurs.
(b) Determine the maximum tensile stress \sigma _(t) and maximum compressive stress \sigma _(c).
Indicate the location where the maximum tensile and compressive stresses occur.
(c) Determine the maximum shear stress \tau _(max) in the web of the beam. Indicate the
location where the maximum shear stress occurs.
(d) Determine the principal stresses and principal strains for the point located at (h)/(2)
above the bottom of the cross section that is just right of point D.
(e) Derive the equation of the deflection curve by using the bending-moment
equation, and then obtain formulas for the deflection \delta _(D) and the angles of
rotation \theta _(A) and \theta _(B) at the supports.
(f) Calculate the total strain energy stored in this beam.