PLAIN AND CIVIL: EXAMPLE 4.3.12. BEAM SUPPORT REACTIONS FOR CONCENTRATED LOADS AND SELF-WEIGHT

Thursday 28 March 2019

A 300mm x 300mm concrete beam carries a 20-kN load 3m from the right support. Determine the support reactions when the beam is 10m long.

In order to determine the self-weight of the beam, one should identify the unit weight of concrete. Unit weight is the ratio of the weight with the volume.

$\gamma_{conc} =\frac{wt}{vol}=2400\frac{kg}{m^{3}}x\frac{10N}{kg}x\frac{kN}{1000N}=24\frac{kN}{m^{3}}$

The total weight of the beam is determined by multiplying the unit weight of the beam material and its volume.

$P=\gamma _{conc}Vol=24\frac{kN}{m^{3}}\left ( 10m \right )\left ( 0.30m \right )\left ( 0.30m \right )=21.60kN$

This weight of the beam is located at the centroid (midpoint).

The FBD of the beam becomes:

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

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

$\sum M_{B}=0$

$R_{AY}\left ( 10m \right )-P\left ( 5m \right )-12kN\left ( 3m \right )=0$

$R_{AY}\left ( 10m \right )=21.60kN\left ( 5m \right )+12kN\left ( 3m \right )$

${\color{Red} \mathbf{R_{AY}=14.40kN}}$

$\sum M_{A}=0$

$P\left ( 5m \right )+12kN\left ( 7m \right )-R_{B}\left ( 10m \right )=0$

$R_{B}\left ( 10m \right )=21.60kN\left ( 5m \right )+12kN\left ( 7m \right )$

${\color{Red} \mathbf{R_{B}=19.20kN}}$

RELATED TOPIC:

4.0. SHEAR AND MOMENT IN BEAMS

PLAIN AND CIVIL

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Thursday 28 March 2019

EXAMPLE 4.3.12. BEAM SUPPORT REACTIONS FOR CONCENTRATED LOADS AND SELF-WEIGHT

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