Solution

What you should know before starting this example: charts for Simple Beams.

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

Reactions

Chart of shear forces and bending moments

Dimensioning and calculating stresses

$\begin{aligned}\\ &k_g=200MPa\\ &I_{y_c}=2\cdot [\frac{2a\cdot a^3}{36}+\frac{1}{2} \cdot 2a\cdot a\cdot {(\frac{a}{3})}^2]=0,33a^4\\ &W_y=\frac{J_{y_c}}{z}=0,33a^3\\ &\sigma=\frac{M_y}{W_y} \le k_g \Rightarrow \frac{101,25\cdot 10^3}{0,33\cdot a^3} \le 200\cdot 10^6\\ &a \ge 0,115m\\ &a=11,6cm\\ \end{aligned}$

Stresses at the lower and upper edge are the same:

\sigma = \frac{101,25\cdot 10^3}{0,33\cdot 0,116^3}=196,56\ MPa

$\begin{aligned}\\ &|\sigma_B|=|\sigma_A|\\ \end{aligned}$

Stress chart

Bending

Strength of materials - Bending - Example 4

Example 4