Question
Asked Aug 28, 2019
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Question 2
A propped cantlever beam in Figure Q2 is loaded by a triangularly distrnbuted load of
maximum intensity qo kN/m at B
Use the fourth-order differental equation of the deflection curve to find expressions for
reactions at A and B,
21
Determine the equation of the deflection curve.
22
A
L
Figure Q2
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Question 2 A propped cantlever beam in Figure Q2 is loaded by a triangularly distrnbuted load of maximum intensity qo kN/m at B Use the fourth-order differental equation of the deflection curve to find expressions for reactions at A and B, 21 Determine the equation of the deflection curve. 22 A L Figure Q2

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Expert Answer

Step 1

(2.1)

For equilibrium conditions, determine the directions of reactions at points A (RA) and B (RB) and the direction of moment reaction at point A (MA). Draw the loading diagram for the cantilever propped beam considering a section X-X at a distance x from point A of the beam. Also, determine the respective load at the X-X section using similar triangle property.

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X 19X-X X R 4x-x

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Step 2

Consider downward loading to be negative and upward loading to be positive. Write the fourth order differential equation for the X-X section, which states that fourth integral of the load will be equal to deflection (Y).

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d'Y (1) EI -x-x = NA 4 L on both sides to obtain the shear force (Fr_y ) equation Integrate the above equation d'Y d N.A EI ddx L d'Y (EIN) dr (2) +C 2L X-X

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Step 3

Integrate the above equation on both sides to ...

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d d'y drdx2 (EIx.A) + N 2L d2Y = Mx- EI +CxC 6L N.A.) X-хX -90r3 + C)х + C, 6L (3) X-X Integrate the above equation to obtain the equation for the slope r_y - X-X d (dY dd -4xGC+C x+C (Ely,A (EIn. 6L dY (EINA + 24L 2 N.A.)dx I0x (ElNAx- + (4) Cx C 2 N.A X-X 24L

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