Beam Analysis and Reaction Forces

Front

Equation for moments in Worked Example No. 1: (Rb x 5) - (60 x 4) - (20 x 2) = 0

Back

Rb = 56 kN

Front

Vertical forces equation: Σ Fy = 0

Back

Ra + Rb - 20 - 60 = 0.

Front

Calculate the reaction forces Ra and Rb.

Back

Ra = 24 kN

Rb = 56 kN

Front

Vertical forces equation in the Example

Back

Ra = 0.75 kN

Rb = 0.25 kN

Front

The sum of moments and forces must equal zero for equilibrium.

Back

This is a fundamental principle in statics.

Front

Uniform loads can be replaced with an equivalent point load.

Back

Front

The total load of 10 kN is equivalent to a single point load at the middle.

Back

Front

Solving for Ra: 4Ra = 20, Ra = 5 kN

Back

Front

Solving for Rb: 5 + Rb - 10 = 0, Rb = 5 kN

Back

Front

The concept of replacing uniform loads simplifies calculations.

Back