Problem 1 A simply supported prismatic beam AB carries a uniformly distributed load w per unit length. Determine: d¹y dx4 (a) Start with the EI =-w and integrate it twice to ,d²y get to El = M(x)=?. Show what? is. dx² a. Hint: What is the moment at both ends? B 000 (b) Derive the Moment equation and does it match the solution you got for (a) (c) Equation of the elastic curve in variables by integrating your solution for (a) twice more and solving for the last two constants of integration. (d) The maximum deflection of the beam in variables

Structural Analysis
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ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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Problem 1
A simply supported prismatic beam AB carries a uniformly
distributed load w per unit length. Determine:
d¹y
(a) Start with the EI=-w and integrate it twice to
,d²y
dx4
get to El= M(x)=?. Show what? is.
dx²
a. Hint: What is the moment at both ends?
(b) Derive the Moment equation and does it match the solution you got for (a)
(c) Equation of the elastic curve in variables by integrating your solution for (a) twice more and
solving for the last two constants of integration.
(d) The maximum deflection of the beam in variables
W
Answer: (a) y = 24 (−x¹ + 2Lx² − Ľ³x) (b) \y\max
24EI
B
5wL4
38EI
Transcribed Image Text:Problem 1 A simply supported prismatic beam AB carries a uniformly distributed load w per unit length. Determine: d¹y (a) Start with the EI=-w and integrate it twice to ,d²y dx4 get to El= M(x)=?. Show what? is. dx² a. Hint: What is the moment at both ends? (b) Derive the Moment equation and does it match the solution you got for (a) (c) Equation of the elastic curve in variables by integrating your solution for (a) twice more and solving for the last two constants of integration. (d) The maximum deflection of the beam in variables W Answer: (a) y = 24 (−x¹ + 2Lx² − Ľ³x) (b) \y\max 24EI B 5wL4 38EI
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