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

Shear and bending moment diagrams

Stresses

The moment diagram is on the side of the tensile fibers. In the most loaded section, the upper fibers are in tension, so the positive normal stresses are at the top of the section, negative at the bottom.

$\begin{aligned}\\ &I_{y_c}=\frac{a\cdot (0,5\cdot a\sqrt3)^3}{36}=0,018a^4\\ &W_y^+=\frac{J_{y_c}}{ż^+}=\frac{0,018a^4}{\frac{2}{3}\cdot (\frac{1}{2}\sqrt3)\cdot a}=0,0312a^3\\ &W_y^-=\frac{J_{y_c}}{ż^-}=\frac{0,013a^4}{\frac{1}{3}\cdot(\frac{1}{2}\sqrt3)a}=0,0623a^3\\ &|\sigma^+|=\frac{My}{W_y^+}=\frac{80\cdot 10^3}{0,0312a^3} \le 180\cdot 10^6 & \Rightarrow & a \ge 0,242m\\ &|\sigma^-|=\frac{My}{W_y^-}=\frac{80\cdot 10^3}{0,0623a^3} \le 180\cdot 10^6 & \Rightarrow & a \ge 0,22m\\ &a=0,25\ m\\ \end{aligned}$

Bending

Strength of materials - Bending - Example 5

Example 5