Problem #$1$

Consider the beam ABCD, with the left end A fixed, a roller at $C,$ a downward force of $4P$ applied at

$B,$ and a downward force of $P$ applied at $D.$ The lengths of segments $|AB|,|BC|,$ and $|CD|$ are all equal to

$\frac{L}{2}.$ Let the constant representing the flexural rigidity be denoted as EI$.$

a$)$ What are the boundary conditions at support A$?$

b$)$ What is the boundary condition at C$?$

c$)$ Utilizing the equilibrium equations for forces and moments, analyze the nature of this beam. Is it

determinate or indeterminate?

d$)$ Determine the reaction forces at A and $C.$ Express the values of the moment at $A(M_A),$ the vertical

reaction force at $A(R_A),$ and the vertical reaction force at $C(R_C)$ as follows: $?).$

$4P,P$

A $,$ B $,$ C $,$ D

L$/2$ L$/2$ L$/2$