please solve the paractice Elastic Deflection By Energy Method Example: Find the vertical displacement of free...
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The governing differential equation for the deflection of a cantilever beam subjected to a point load at its free end (Fig. 1) is given by: 2 dx2 where E is elastic modulus, Izz is beam moment of inertia, y 1s beam deflection, P is the point load, and x is the distance along the beam measured from the free end. The boundary conditions are the deflection y(L) is zero and the slope (dy/dx) at x-L...
PROBLEM #1: (50 points) Using Castigliano's method, determine the vertical deflection of the free end, point C, due to the vertical force F applied at point B of the step cantilever shaft shown in the figure. The second area moments for sections AB and BC are 1 and 21, respectively. 1/2 1/2
Assignment: 25 Marks Using the general stiffness method, calculate the deflection of the free end of the cantilever beam shown in the figure below. Use the slope deflection equations to prove that the moment at the support = 2WL2 and the moment at the position where stiffness changes = 0.5 wite EI Hint: constrain the freedom of movement as indicated 17wL 16 EI Answer:
Assignment: 25 Marks Using the general stiffness method, calculate the deflection of the free end of...
Using the theorem of Castigliano, find the vertical and horizontal deflection of the free end at point d due to the horizontal applied load F for the cantilever frame shown in the figure. Express your answers in terms of F, I, I, E (modulus of elasticity), 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 sectional is circular. be ay
4. Use singularity function method to solve the problem. The cantilever beam has modulus of elasticity E and bending moment of inertia I. (1) Draw the free body diagram of the beam (2pts). (2) Find the reactions at the supports (3pts). (3) Find the loading (intensity of load) of the beam in singularity function form (4 pts). (4) What is the vertical shear function like? (4pts) (5) Houw much is the moment? (4pts) (6) Express the elastic curve of the...
Problem 1: Use the principal of work and energy to find the vertical deflection of the simply supported beam under the applied concentrated load. EI is constant 30 kN A 3 m 7 m B
Using equation 3 please find the deflection value with the
variables given. Be careful with units please.
P= 10.07 Newtons
L= 953.35 mm
x= 868.363 mm
E= 72.4 GPa
Iy= 5926.62 mm^4
The maximum deflection, WMAX of the cantilever beam occurs at the free end. The magnitude of the deflection may be derived by solving the differential equation: d'w M,(x) P (L-x) eq. 1 dr EI EI where E and Iy are the modulus of elasticity and moment of inertia...
Cantilever beam under a concentrated load. One end is fixed. Solve for the deflection and stress of the cantilever. y= 1/EI [-1/6Fx^3 + 1/2FL^2x - 1/3FL^3] E Modulus of Elasticity 70 GPa I Second Moment of Inertia (bh^3)/12 Length 0.55m Height 0.0127m Thickness 0.0635m Load m=4.53kg applied 0.0325m away from the free end and gravity = 9.81m/s^2
10. The slope and deflection at a section in a loaded beam can be found out by which of the following methods? (a) Double integration method (b) Moment area method (c) Macaulay's method (d) Any of the above. 15. A cartilever AB of length 1 is carrying a distributed load whose intensity varies uniformly from zero at the free end to w per un run at the forced end. The deflection at the free end is given as: (3) 30E1...
PLEASE SOLVE USING MATLAB
The basic differential equation of the elastic curve for a cantilever beam as shown is given as 2 da2 where E = the modulus of elasticity and-the moment of inertia. Show how to use MATLAB ODE solvers to find the deflection of the beam. The following parameter values apply (make sure to do the conversion and use in as the Unit of Length in all calculations): E = 30,000 ksi, I = 800 in4, P-1 kips,...