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Question-183527




Question Number 183527 by aurpeyz last updated on 26/Dec/22
Commented by aurpeyz last updated on 26/Dec/22
The bar is under the action of axial   concentrated force P and 2P (P=10KN).  Area of constant cross section of bar is  equal F, Young′s modulus of bar material  is equal E.   Determine the maximum value of the   longitudinal force N_x  in the power sections.  a. 12.5KN  b. 10KN  c. 20KN  d. 30KN
$${The}\:{bar}\:{is}\:{under}\:{the}\:{action}\:{of}\:{axial}\: \\ $$$${concentrated}\:{force}\:{P}\:{and}\:\mathrm{2}{P}\:\left({P}=\mathrm{10}{KN}\right). \\ $$$${Area}\:{of}\:{constant}\:{cross}\:{section}\:{of}\:{bar}\:{is} \\ $$$${equal}\:{F},\:{Young}'{s}\:{modulus}\:{of}\:{bar}\:{material} \\ $$$${is}\:{equal}\:{E}.\: \\ $$$${Determine}\:{the}\:{maximum}\:{value}\:{of}\:{the}\: \\ $$$${longitudinal}\:{force}\:{N}_{{x}} \:{in}\:{the}\:{power}\:{sections}. \\ $$$${a}.\:\mathrm{12}.\mathrm{5}{KN} \\ $$$${b}.\:\mathrm{10}{KN} \\ $$$${c}.\:\mathrm{20}{KN} \\ $$$${d}.\:\mathrm{30}{KN} \\ $$
Commented by mr W last updated on 26/Dec/22
what do you mean with “power”   sections?
$${what}\:{do}\:{you}\:{mean}\:{with}\:“{power}''\: \\ $$$${sections}? \\ $$
Answered by mr W last updated on 26/Dec/22
say the axial force in section D is x.  ((x×2a)/(EF))+(((x+P)×a)/(EF))+(((x+P−2P)×a)/(EF))=0  2x+x+P+x−P=0  ⇒x=0  in CD: N_x =x=0  in BC: N_x =x+P=P=10 KN  in AB: N_x =x+P−2P=−P=−10 KN  ⇒answer b
$${say}\:{the}\:{axial}\:{force}\:{in}\:{section}\:{D}\:{is}\:{x}. \\ $$$$\frac{{x}×\mathrm{2}{a}}{{EF}}+\frac{\left({x}+{P}\right)×{a}}{{EF}}+\frac{\left({x}+{P}−\mathrm{2}{P}\right)×{a}}{{EF}}=\mathrm{0} \\ $$$$\mathrm{2}{x}+{x}+{P}+{x}−{P}=\mathrm{0} \\ $$$$\Rightarrow{x}=\mathrm{0} \\ $$$${in}\:{CD}:\:{N}_{{x}} ={x}=\mathrm{0} \\ $$$${in}\:{BC}:\:{N}_{{x}} ={x}+{P}={P}=\mathrm{10}\:{KN} \\ $$$${in}\:{AB}:\:{N}_{{x}} ={x}+{P}−\mathrm{2}{P}=−{P}=−\mathrm{10}\:{KN} \\ $$$$\Rightarrow{answer}\:{b} \\ $$
Commented by aurpeyz last updated on 27/Dec/22
thanks
$${thanks} \\ $$

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