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Sketch-the-shear-and-moment-diagrams-of-a-simply-supported-beam-of-6m-The-load-on-the-beam-consists-of-UDL-of-15KN-m-over-the-left-half-of-the-span-




Question Number 68222 by necxxx last updated on 07/Sep/19
Sketch the shear and moment diagrams  of a simply supported beam of 6m.The  load on the beam consists of UDL of  15KN/m over the left half of the span.
$${Sketch}\:{the}\:{shear}\:{and}\:{moment}\:{diagrams} \\ $$$${of}\:{a}\:{simply}\:{supported}\:{beam}\:{of}\:\mathrm{6}{m}.{The} \\ $$$${load}\:{on}\:{the}\:{beam}\:{consists}\:{of}\:{UDL}\:{of} \\ $$$$\mathrm{15}{KN}/{m}\:{over}\:{the}\:{left}\:{half}\:{of}\:{the}\:{span}. \\ $$$$ \\ $$
Commented by necxxx last updated on 07/Sep/19
please help me with this problem. I′ve  tried solving but my result isnt in   accordance with the source. Please post  steps and diagrams where necessary.  I′ll also post the steps I took so you all can   help me with the amendments.  Thanks in advance.
$${please}\:{help}\:{me}\:{with}\:{this}\:{problem}.\:{I}'{ve} \\ $$$${tried}\:{solving}\:{but}\:{my}\:{result}\:{isnt}\:{in}\: \\ $$$${accordance}\:{with}\:{the}\:{source}.\:{Please}\:{post} \\ $$$${steps}\:{and}\:{diagrams}\:{where}\:{necessary}. \\ $$$${I}'{ll}\:{also}\:{post}\:{the}\:{steps}\:{I}\:{took}\:{so}\:{you}\:{all}\:{can}\: \\ $$$${help}\:{me}\:{with}\:{the}\:{amendments}. \\ $$$${Thanks}\:{in}\:{advance}. \\ $$
Commented by necxxx last updated on 07/Sep/19
Commented by necxxx last updated on 07/Sep/19
Commented by necxxx last updated on 07/Sep/19
Commented by necxxx last updated on 07/Sep/19
here is the diagram given
$${here}\:{is}\:{the}\:{diagram}\:{given} \\ $$$$ \\ $$
Answered by mr W last updated on 07/Sep/19
Commented by necxxx last updated on 07/Sep/19
Thank you so much sir but this SFD  and BMD do not tally with the answer  given in the reference material I used.
$${Thank}\:{you}\:{so}\:{much}\:{sir}\:{but}\:{this}\:{SFD} \\ $$$${and}\:{BMD}\:{do}\:{not}\:{tally}\:{with}\:{the}\:{answer} \\ $$$${given}\:{in}\:{the}\:{reference}\:{material}\:{I}\:{used}. \\ $$$$ \\ $$
Commented by mr W last updated on 07/Sep/19
the values i gave are 100% corrrect,  that′s for sure.  your book might use different signs.  therefore i haven′t given any sign for  the values.
$${the}\:{values}\:{i}\:{gave}\:{are}\:\mathrm{100\%}\:{corrrect}, \\ $$$${that}'{s}\:{for}\:{sure}. \\ $$$${your}\:{book}\:{might}\:{use}\:{different}\:{signs}. \\ $$$${therefore}\:{i}\:{haven}'{t}\:{given}\:{any}\:{sign}\:{for} \\ $$$${the}\:{values}. \\ $$
Commented by necxxx last updated on 07/Sep/19
Commented by mr W last updated on 07/Sep/19
if the maximum of moment is needed,  it is  ((135)/4)×(9/4)−(1/2)×15×((9/4))^2 =((1215)/(32))=37.97 KNm  which is there where the shear force  is zero.
$${if}\:{the}\:{maximum}\:{of}\:{moment}\:{is}\:{needed}, \\ $$$${it}\:{is} \\ $$$$\frac{\mathrm{135}}{\mathrm{4}}×\frac{\mathrm{9}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{15}×\left(\frac{\mathrm{9}}{\mathrm{4}}\right)^{\mathrm{2}} =\frac{\mathrm{1215}}{\mathrm{32}}=\mathrm{37}.\mathrm{97}\:{KNm} \\ $$$${which}\:{is}\:{there}\:{where}\:{the}\:{shear}\:{force} \\ $$$${is}\:{zero}. \\ $$
Commented by mr W last updated on 07/Sep/19
in fact i drawed the sketches without  any calculation.
$${in}\:{fact}\:{i}\:{drawed}\:{the}\:{sketches}\:{without} \\ $$$${any}\:{calculation}. \\ $$
Commented by necxxx last updated on 07/Sep/19
ok.Thank you so much.I′ll try to study  it more
$${ok}.{Thank}\:{you}\:{so}\:{much}.{I}'{ll}\:{try}\:{to}\:{study} \\ $$$${it}\:{more} \\ $$
Commented by mr W last updated on 07/Sep/19
the value given in your book for M_(max)   is wrong. it is not 37.37 KNm, but  37.97 KNm. other values in your  book are correct and tally with my  results.
$${the}\:{value}\:{given}\:{in}\:{your}\:{book}\:{for}\:{M}_{{max}} \\ $$$${is}\:{wrong}.\:{it}\:{is}\:{not}\:\mathrm{37}.\mathrm{37}\:{KNm},\:{but} \\ $$$$\mathrm{37}.\mathrm{97}\:{KNm}.\:{other}\:{values}\:{in}\:{your} \\ $$$${book}\:{are}\:{correct}\:{and}\:{tally}\:{with}\:{my} \\ $$$${results}. \\ $$
Commented by necxxx last updated on 08/Sep/19
please how did you do that.Really I would   like to know how you solved it  comprehensively.      Thanks
$${please}\:{how}\:{did}\:{you}\:{do}\:{that}.{Really}\:{I}\:{would}\: \\ $$$${like}\:{to}\:{know}\:{how}\:{you}\:{solved}\:{it} \\ $$$${comprehensively}. \\ $$$$ \\ $$$$ \\ $$$${Thanks} \\ $$
Commented by necxxx last updated on 09/Sep/19
Thank you so much MrW.After looking  at the solvings you made I went further  to practice and now I understand to a  good extent.
$${Thank}\:{you}\:{so}\:{much}\:{MrW}.{After}\:{looking} \\ $$$${at}\:{the}\:{solvings}\:{you}\:{made}\:{I}\:{went}\:{further} \\ $$$${to}\:{practice}\:{and}\:{now}\:{I}\:{understand}\:{to}\:{a} \\ $$$${good}\:{extent}. \\ $$

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