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

\]

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