PLAIN AND CIVIL: EXAMPLE 7.0.8. FINDING REACTIONS

Saturday 9 March 2019

EXAMPLE 7.0.8. FINDING REACTIONS

Neglecting the beam thickness, determine the support reactions at the supports.

First thing to do is to check that the number of available equations of equilibrium is sufficient to solve the required or unknowns in the system. Do this by identifying how many unknowns are present.

At point A is a hinge which reacts vertically and horizontally, that is, two unknowns from reaction A. Point B has a roller reacting only vertically or perpendicularly on the surface, meaning 1 unknown. Total of 3 unknowns in the system can be solved with the 3 equations of equilibrium.

After identifying how many unknowns are in the system, go ahead and assume how these reactions are directed - either left of right, either up or down. You assumptions, although just hypotheses, are dependent on the applied loads present.

The next step is to simplify inclined forces to easily identify the perpendicular distances when applying resultant moments.

$F_{x}=\frac{3}{5}500lb=300lb$

$F_{y}=\frac{4}{5}500lb=400lb$

Equilibrium equation for horizontal forces can be used as there is only 1 unknown.

$\sum F_{x}=0\rightarrow$

$F_{x}-Rx_{a}=0$

   ${\color{Red} \mathbf{Rx_{a}=300lb}}$

However, using   $\sum F_{y}=0\uparrow$ will only lead to an equation with two unknowns.

The better thing to do is to work with $\sum M=0$ .

   $\sum M_{B}=0$

   $Ry_{a}\left ( 10ft \right )-F_{y}\left ( 5ft \right )+600lb-ft=0$

   $Ry_{a}\left ( 10ft \right )=400lb\left ( 5ft \right )-600lb\cdot ft$

   ${\color{Red} \mathbf{Ry_{a}=140lb\cdot ft}}$

Do similar procedure to take the reaction at the roller at point B.

$\sum M_{A}=0$

   $F_{y}\left ( 5ft \right )-R_{B}\left ( 10ft \right )+600lb\cdot ft=0$

   $R_{B}\left ( 10ft \right )=400lb\left ( 5ft \right )+600lb\cdot ft$

${\color{Red} \mathbf{R_{B}=260lb}}$

RELATED TOPIC:

7.0 EQUILIBRIUM OF FORCE SYSTEMS