What you should know before starting this example: charts for Straight beams.

Understanding this example will be aided by video courses from Example 1 and Example 2.

Reactions

$\begin{aligned}\\ &\sum{M_{A}}=0 & 10\cdot 4\cdot\ 2-V_B\cdot 4+15\cdot 6=0 & V_B=42,5\ kN\\ &\sum{M_{B}}=0 & V_A\cdot 4-10\cdot 4\cdot 2+15\cdot 2=0 & V_A=12,5\ kN\\ \end{aligned}$

\begin{aligned}\\ &\frac{12,5}{x}=\frac{27,5}{4-x}\\ &x=1,25m\\ &M_{max}=V_A\cdot 1,25-10\cdot 1,25\cdot \frac{1,25}{2}=7,8125\ kNm\\ \end{aligned}

Chart of shear forces and bending moments

Stress chart

For the most loaded section (B) – the largest bending moment

\begin{aligned}\\ &\sigma=\frac{M_Y}{W_Y}\\ &W_y=\frac{bh^2}{6}=\frac{0,1\cdot (0,15)^2}{6}=3,75\cdot 10^{-4}\\ &\sigma_g=\frac{30\cdot 10^3}{3,75\cdot 10^{-4}}=+80\ MPa\\ \\ \end{aligned}

Due to symmetry:

\begin{aligned}\\ &\\ &\sigma_d=-\sigma_g=-80\ MPa \end{aligned}

Bending

Strength of materials - Bending - Example 3

Example 3