4.5-6 The simple beam AB shown in the figure is subjected to a concentrated load P and a clockwise couple M, = PL/3 acting at the third points. Draw the shear-force and bending-moment diagrams for this beam. PL 3 A 3 PROBLEM 4.5-6

The beam in the figure below is subjected to a load P = 3.5 kN at its end. Young’s modulus is 210 GPa and the moment of inertia for the beam’s cross-section is 5×106 mm4.  If a = 1.5 m and b = 0.6 m, determine: a) Reaction value at support A. Positive direction is considered upwards. b) moment equation M(x1) in the segment AB, where x1 changes from 0 at support A to a at support B. Enter the equation in terms of variables P, a, band x1. c) moment equation M(x2) in the segment BC, where x2 changes from 0 at point C to b at support B. Enter the equation in terms of variables P, a, band x2. d) the value of the constant of integration C1 e) the value of the constant of integration C2 f) the value of the constant of integration C3 g) the value of the constant of integration C4 h) the value of displacement at point C i) the position of maximum displacement in the segment AB j) the value of maximum displacement in the segment AB

The cross-sectional dimensions of a beam are shown in the figure. Assume a = 45 mm, b = 75 mm, t = 4 mm and d =55 mm. (a) If the bending stress at point Kis 54 MPa (C), determine the internal bending moment M₂ acting about the z centroidal axis of the beam. (b) Determine the bending stress at point H. The bending stress is positive if in tension and negative if in compression. IT H Answers: (a) M₂= (b) og = i 945.9 144.881 d N-m MPa

In the following figure, there are two equal couples with a magnitude of M = 15 kNm. They act in opposite directions while being applied to the channel beam AB. These couples cause the beam to bend in the horizontal plane. Find: 1) Stress at point C 2) Stress at point D 3) Stress at point E