problem. find the reactions at pin support a and at roller support c for the simply supported beam under the…

Explanation:

Step1: Sum of vertical - forces

Let the vertical reaction at $A$ be $A_y$ and at $C$ be $C_y$. The sum of vertical forces $\sum F_y=0$. $A_y + C_y-10 - 4-2=0$, so $A_y + C_y=16$ kips.

Step2: Sum of moments about $A$

The sum of moments about point $A$, $\sum M_A = 0$. Taking counter - clockwise moments as positive. $C_y\times(4 + 3)-10\times4-4\times(4 + 3/2)-2\times(4 + 3+3)-624/12=0$. $7C_y-40 - 4\times5.5-2\times10 - 52=0$. $7C_y-40-22 - 20 - 52=0$. $7C_y-(40 + 22+20 + 52)=0$. $7C_y-134 = 0$. $C_y=\frac{134}{7}\approx19.14$ kips.

Step3: Find $A_y$

Substitute $C_y$ into the $\sum F_y = 0$ equation. $A_y=16 - C_y$. $A_y=16-\frac{134}{7}=\frac{112 - 134}{7}=-\frac{22}{7}\approx - 3.14$ kips.

Answer:

The vertical reaction at $A$ is $A_y\approx - 3.14$ kips and at $C$ is $C_y\approx19.14$ kips.