Consider a 3 metre long uniform beam with flexural rigidity of 100 kNm². The beam is supported with a fixed (clamped) support on the left, and a roller support 1 metre from the right hand side. TITIT Om 3m A 1kN/m point load is applied 1 metre from the left hand side. If we find the deflection for this beam, using the boundary conditions for the fixed (clamped) end and for the roller support, we get the equation. y(z) = 9600 ((162³-482² +48r - 16) H(z − 1) – 112³ + 182²) Om 2m (you do not need to calculate this yourself, but you may verify it if you wish) 2m Have Desmos (or any other computer graphing system you like) draw a picture of the beam under load. Make sure the picture is accurate, and is zoomed appropriately to see the actual bends in the curve. What is wrong with the deflection function to the right of the roller support? b) Solve the deflection for this beam in two parts, as if there were two separate beams: Y For the roller support use the following boundary conditions: y (2)=0 and y'(2) => where A is an unknown real constant (i.e., AR) used to ensure that both solutions have the same derivative at the roller support. You should get two different deflection functions: YL (1) and yr (1). The function yr is the deflection calculated for the left two-thirds of the beam, and the function yr is the deflection calculated for the right one-third of the beam. The deflection for the whole beam is given by y(z) [YL (1) if 0
Consider a 3 metre long uniform beam with flexural rigidity of 100 kNm². The beam is supported with a fixed (clamped) support on the left, and a roller support 1 metre from the right hand side. TITIT Om 3m A 1kN/m point load is applied 1 metre from the left hand side. If we find the deflection for this beam, using the boundary conditions for the fixed (clamped) end and for the roller support, we get the equation. y(z) = 9600 ((162³-482² +48r - 16) H(z − 1) – 112³ + 182²) Om 2m (you do not need to calculate this yourself, but you may verify it if you wish) 2m Have Desmos (or any other computer graphing system you like) draw a picture of the beam under load. Make sure the picture is accurate, and is zoomed appropriately to see the actual bends in the curve. What is wrong with the deflection function to the right of the roller support? b) Solve the deflection for this beam in two parts, as if there were two separate beams: Y For the roller support use the following boundary conditions: y (2)=0 and y'(2) => where A is an unknown real constant (i.e., AR) used to ensure that both solutions have the same derivative at the roller support. You should get two different deflection functions: YL (1) and yr (1). The function yr is the deflection calculated for the left two-thirds of the beam, and the function yr is the deflection calculated for the right one-third of the beam. The deflection for the whole beam is given by y(z) [YL (1) if 0
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Consider a 3 metre long uniform beam with flexural rigidity of 100 kNm². The beam is supported with a
fixed (clamped) support on the left, and a roller support 1 metre from the right hand side.
3m
2m
A 1kN/m point load is applied 1 metre from the left hand side.
If we find the deflection for this beam, using the boundary conditions for the fixed (clamped) end and for
the roller support, we get the equation.
y(z) 9600 ((16³-48x² +48r - 16) H(r− 1) - 112³ +18r²)
(you do not need to calculate this yourself, but you may verify it if you wish)
Have Desmos (or any other computer graphing system you like) draw a picture of the
beam under load. Make sure the picture is accurate, and is zoomed appropriately to see the actual
bends in the curve.
What is wrong with the deflection function to the right of the roller support?
b)
Solve the deflection for this beam in two parts, as if there were two separate beams:
3m
Om
2m
2m
For the roller support use the following boundary conditions:
y (2)= 0 and y(2) =>
where A is an unknown real constant (i.e., AR) used to ensure that both solutions have the same
derivative at the roller support.
You should get two different deflection functions: yr (r) and yr (r). The function yr is the deflection
calculated for the left two-thirds of the beam, and the function yr is the deflection calculated for
the right one-third of the beam.
The deflection for the whole beam is given by
y(x)
[YL(x) if 0<x<2
YR(r) if 2 <r <3
Find the value of X corresponding to the beam.
Does this deflection function have the same problem that the one above had?
477 5
Om
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