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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.


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