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Q4. A prismatic beam AB is subjected to a couple moment $M_o$ and an axial load P. By considering the normal stress only and using first principles, derive the general equation for the strain energy of the beam. The beam has a cross-sectional area of A, and a Young's Modulus of E. P D $M_o$ a b L B P [Q4: 91 marks]

Name: q4 a prismatic beam ab is subjected to a couple moment mo and an axial load p by considering the normal stress only and using first principles derive the general equation for the strain ene 67246
Uploaded: 2023-08-01T06:43:35-08:00
Duration: 1 min 38 s
Channel: Supreeta N
Description: q4 a prismatic beam ab is subjected to a couple moment mo and an axial load p by considering the normal stress only and using first principles derive the general equation for the strain ene 67246

          Q4. A prismatic beam AB is subjected to a couple moment $M_o$ and an axial load P. By considering the normal stress only and using first principles, derive the general equation for the strain energy of the beam. The beam has a cross-sectional area of A, and a Young's Modulus of E.
P
D
$M_o$
a
b
L
B
P
[Q4: 91 marks]

q4 a prismatic beam ab is subjected to a couple moment mo and an axial load p by considering the normal stress only and using first principles derive the general equation for the strain ene 67246

Added by Christina J.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Supreeta N

08/01/2023

Step 1

In this case, $N(x) = P$ for all $x$, so $$U_P = \int_0^L \frac{P^2}{2AE} dx = \frac{P^2}{2AE} \int_0^L dx = \frac{P^2 L}{2AE}$$ Show more…

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Q4. A prismatic beam AB is subjected to a couple moment $M_o$ and an axial load P. By considering the normal stress only and using first principles, derive the general equation for the strain energy of the beam. The beam has a cross-sectional area of A, and a Young's Modulus of E. P D $M_o$ a b L B P [Q4: 91 marks]