For the force P in the figure, determine the components P1 and P2, if the former is directed 80° from the horizontal axis( a-axis) and the latter 20° to the same reference axis. Force P=45 kN is acting at a given angle of 60° from the x axis.

The beam with cross-section shown in Figure 1 is subjected to a uniformly distributed load and a moment. The centroidal axis of the section is c= 74.44 mm from the bottom. I. -2.18x10 mm. E = 2.1×10 MPa. a) At a cross-section 2 m to the right of support A; i) ii) iii) Calculate the Shear Force, V, and the Bending Moment, M. Determine the maximum bending stress. Sketch the bending stress distribution across the section, include critical tension & compression stress values. Determine shear stress developed at the flange-web interface and also the shear stress at the neutral axis of the cross-section. Sketch the shear stress distribution across the section, include the critical values. b) Using the double integration method, find the deflection curve for 0≤x≤5 m. 3 kN/m 5m 3 m- Figure 1 15 kN-m 100 All dimensions are in mm.

There is a beam subject to a uniform force w as shown in the figure below. The E of the entire section is 200 GPa and I is 60x10^6 mm^4. (a) Calculate the reaction force at point c and the vertical displacement at point B (b) If the support point C sinks downward by 0.1m for some reason, calculate the reaction force at point C and the vertical displacement of point B.

F1 F2 b M a C A a a Given the system above, F1 = 34 N, F2 = 96 N, M = 245 N-m, a = 3 m, b = 2 m, and a = 40°. %3D (a) Represent the system using a single force. Determine the magnitude of the force and its location relative to point A. Round all answers to the nearest integer. The magnitude of the force (N) is: N The position of the force relative to A (m) is: m (b) Represent the system using a force and a couple moment acting at point C. Determine the magnitudes of the force and the couple moment. Round all answers to the nearest integer. The magnitude of the force (N) is: N The magnitude of the couple moment (N-m) is: N-m