YT Version

Classic Version

\begin{aligned} &\sum{Y}=0\\ &15-5-10\cdot 6 + V_{D} = 0\\ &V_{D}=50 \ kN\\ &\sum{M_{D}}=0\\ &M_{A} + 15\cdot 6\cdot 3 - 10\cdot 6\cdot 3 +10=0\\ &M_{A}=95 \ kNm\\ \end{aligned}

Interval AB \(x \in{\langle 0,2)}\)

\begin{aligned} &Q_{AB}=0\\ &M_{AB}=M_{A}=95\\ \end{aligned}

Interval BC \(2 \leq x >5\)

\begin{aligned} &Q_{BC}=15-10(x-2)\\ &Q_{B}(2)=15\\ &Q_{C}(5)=-15\\ &M_{BC}=M_{A} + 15(x-2) - 10 \bigg(\frac{(x-2)^{2}}{2}\bigg)\\ &M_{B}(2)=95\\ &M_{C}(5)=95\\ &M_{max}(3,5)=106,25\\ \end{aligned}

Interval ED \(x \in{\langle 0,2)}\)

\begin{aligned} &Q_{ED}=0\\ &M_{ED}=-10\\ \end{aligned}

Interval DC \(x \in{\langle 2,5)}\)

\begin{aligned} &Q_{DC}=-V_{D} + 10(x-2)\\ &Q_{D}(2)=-50\\ &Q_{C}(5)=-20\\ &M_{DC}=V_{D}(x-2) - 10\bigg(\frac{(x-2)^{2}}{2}\bigg)-10\\ &M_{D}(2)=-10\\ &M_{C}(5)=95\\ \end{aligned}

Charts

Internal Forces - Beams

Strength of materials - Internal Forces - Beams - Example 7

Example 7