## Bending moments and shear force diagrams

Draw the SFD and BMD diagram for the fallowing simply supported beams. Find the maximum deflection and state if is hogging or sagging.

Calculations:
For SFD Diagram
From the left side: SF=70-10x, x=distance
${SF}_1=70-10\times{}0$
${SF}_1=70kN$
${SF}_2=70-10\times{}1$
${SF}_2=60kN$
${SF}_3=70-10\times{}2$
${SF}_3=50kN$
${SF}_{3(output)}=50-40=10kN$
${SF}_4=70-10\times{}4$
${SF}_4=0kN$
In point of ${SF}_{4 }$ force shifts its magnitude.
From right side: SF=10x-50=distance
${SF}_5=10\times{}0-50$
Load force from top gives -40kN to ${SF}_{4 }$ on the output of liner force on the diagram.
${SF}_5=-50kN$
${SF}_6=10\times{}2-50$
${SF}_6=-30kN$
${SF}_7=10\times{}4-50$
${SF}_7=-10$
${SF}_8=10\times{}5-50$
${SF}_8=0kN$
For BMD diagram
From the left side: $BM=70×r-(10x^2)/2$
${BM}_1=70\times{}1-\frac{10\times{}1}{2}$
${BM}_1=65kNm$
${BM}_2=70\times{}2-\frac{10\times{}4}{2}$
${BM}_2=120kNm$
Calculation from right side:
${BM}_3=50\times{}2-\frac{10\times{}4}{2}$
${BM}_3=80kNm$
${BM}_4=50\times{}4-\frac{10\times{}16}{2}$
${BM}_4=120kNm$
Maximum deflection:
${BM}_5=50\times{}5-\frac{10\times{}25}{2}$
${BM}_5=125kNm$