Using the theorem of Castigliano, find the HORIZONTAL deflection of the free end of the cantilever frame shown in the figure below due to the vertieal applied load P. Express your answers in terms of P, l (lower case L for length), E (modulus of clasticity), A (cross sectional area) and I (moment of inertia of the cross section around the bending axis. Consider only bending and axial loading and assume that the cross-section is circular, E, A, and I are constant.

Solve the problem by the moment-area method. The beam has constant flexural rigidity EI. A simple beam AB supports two concentrated loads P at the positions shown in the figure. B C 4. 4 A support C at the midpoint of the beam is positioned at distance d below the beam before the loads are applied. Assuming that d = 12 mm, L = 5.4 m, E = 200 GPa, and I = 193 x 10° mm, calculate the magnitude of the loads P (in kN) so that the beam just touches the support at C. 163.87 x kN

Considering the solution above, can you help with part (d) 3. The beam shown below has a Young’s modulus of 50 GPa and has a square cross-section of side1 cm. Determine the following using the second-order integration method:(a) Bending moment M(x) along the length of the beam.(b) The slope of the beam θ(x).(c) The deflection of the beam v(x).(d) Slope of the beam at support θB

Using the theorem of Castigliano, find the horizontal deflection of the free end of the cantilever frame shown in the figure below due to the vertical applied load 'P'. Express your answers in terms of P, 1 (lowercase L for length), E (modulus of clasticity), A (cross-sectional area), and I (moment of inertia of the cross section around the bending axis. Consider only bending and axial loading and assume that the cross-section is circular. A, E, and I are constant.

please solve using CASTIGLIANO’s Method   ( Hand written and clean writing )