Calculation of Bending Moments and beam deflection

[mm391]

Homework Statement

The picture of the beam below has a module of rigidity EI, determine the reactions at the supports and the equation of the deflection curve of the left half of the beam

Homework Equations

v*EI=((M_a*x²)/2)+((R_a*x³)/6)

Ʃ of Forces in Y direction = R_a+R_b=0
Ʃ Moments about A = M_a-M_o+M_b-R_a*L

The Attempt at a Solution

How do I go about finding R_a and R_b and M_a and M_b?

For the left had side of the beam the bending moment equation is M_a+R_a*x

Putting x = L/2 into the defelction equation gives me:

((M_a*L^2)/(8EI))=((-R_a*L^3)/(48EI))

 

[SteamKing]

Where's your picture of the beam?

 

[mm391]

Sorry I forgot to add the picture. It should be attached now.

 

[SteamKing]

The beam is statically indeterminate. You'll need to use double integration of the bending moment curve and the boundary conditions at the ends of the beam to solve for the reactions and moments at the ends.

 

[rezeew]

I would first clarify any uncertainties about the given information and equations. For example, I would ask for the units of the given parameters (such as EI) and ensure that all units are consistent throughout the calculations. Additionally, I would verify the assumptions made in the calculation, such as the beam being in a static equilibrium and the material having a linear elastic behavior.

Next, I would use the given equations and apply the principles of equilibrium to solve for the unknown reactions and bending moments. This may involve setting up a system of equations and using algebraic manipulation to solve for the unknown variables.

Once the reactions and bending moments are determined, I would use the equations for bending moments and deflection to calculate the deflection curve of the left half of the beam. This would involve substituting the known values into the equations and solving for the deflection at various points along the beam.

Finally, I would critically evaluate the results to ensure they make sense and are within the expected range. If there are any discrepancies, I would review my calculations and assumptions to identify any potential errors.

In conclusion, as a scientist, I would approach this problem by first clarifying any uncertainties, applying the principles of equilibrium, and critically evaluating the results to ensure accuracy.