PLAIN AND CIVIL: EXAMPLE 4.3.13. BEAM SUPPORT REACTIONS FOR DISTRIBUTED LOADS AND SELF-WEIGHT

A 5m wall, weighing 6kN/m is located on a 300x400m concrete beam. If the beam's length is 8m, determine the support reactions.

Identify the self-weight of the beam.

$Wt_{conc}=\gamma _{conc}\left ( Area \right )=24\frac{kN}{m^{3}}\left ( 0.30m \right )\left ( 0.40m \right )=2.88\frac{kN}{m}$

The FBD of the beam becomes:

$P=6\frac{kN}{m}\left ( 5m \right )=30kN$

$W=2.88\frac{kN}{m}\left ( 8m \right )=23.04kN$

$\sum F_{X}=0]\rightarrow$

${\color{Red} \mathbf{R_{AX}=0}}$

$\sum M_{C}=0$

$R_{AY}\left ( 8m \right )-P\left ( 8-2.5m \right )-W\left ( 4m \right )=0$

$R_{AY}\left ( 8m \right )=30kN\left ( 5.5m \right )+23.04kN\left ( 4m \right )$

${\color{Red} \mathbf{R_{AY}=32.145kN}}$

$\sum M_{A}=0$

$P\left ( 2.5m \right )+W\left ( 4m \right )-R_{C}\left ( 8m \right )=0$

$R_{C}\left ( 8m \right )=30kN\left ( 2.5m \right )+23.04\left ( 4m \right )$

${\color{Red} \mathbf{R_{C}=20.895kN}}$

RELATED TOPIC:

4.0. SHEAR AND MOMENT IN BEAMS

PLAIN AND CIVIL

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Friday 29 March 2019

EXAMPLE 4.3.13. BEAM SUPPORT REACTIONS FOR DISTRIBUTED LOADS AND SELF-WEIGHT

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