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: \[BM=70Śr-(10x^2)/2\]
\[
{BM}_1=70\times{}1-\frac{10\times{}1}{2}
\]
\[
{BM}_1=65kNm
\]
\[
{BM}_2=70\times{}2-\frac{10\times{}4}{2}
\]
\[
{BM}_2=120kNm
\]
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:
\[
{BM}_5=50\times{}5-\frac{10\times{}25}{2}
\]
\[
{BM}_5=125kNm
\]