For the beam in shown in the figure, determine the vertical displacement in C & and the rotation in A using Castigliano's Theorem. E = 200 GPa; 1= 150X10° mm². A 8 kN/m -4 m 20 KN C -4 m- B

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

Two wooden studs with cross-sectional dimensions 45×145 mm2 are glued together to form a beam with a T-section according to the figure on the right and loaded according to the figure on the left. The beam is loaded in its rigid direction. Calculate the moment of inertia of the cross-section about the centroid axis (z-axis). Calculate the maximum normal stress in the beam. Sketch the normal stress distribution over the most loaded cross-section of the beam. All calculations must be clear and handwritten, draw and check so that the answers are correct