Let æ represent the distance from the free end of the beam. Write the moment function in terms of æ using the standard sign convention for beams uhen
Let æ represent the distance from the free end of the beam. Write the moment function in terms of æ using the standard sign convention for beams uhen
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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SOLVE CAREFULLY!! Please Write Clearly and Box the final Answer for Part A, Part B with THE CORRECT UNITS! Thank you Express your answer to three significant figures and include appropriate units.
![Learning Goal:
To use integration to find the equation for the elastic
curve of a beam.
Part A - The moment function
For beams with small deflections, the shape of the
elastic curve is related to the internal bending
d?v
moment by the equation EI = M(x), where
da?
x is the position along the beam as measured from
the free end of the beam, v is the transverse
Let x represent the distance from the free end of the beam. Write the moment function in terms of x using the standard sign convention for beams.
Express your answer so the moment is in kN. m when r is in m.
displacement, E is the elastic modulus of the
• View Available Hint(s)
material, and I is the moment of inertia for the
section. The equation for the elastic curve can be
determined by integrating this equation twice with
respect to x and using boundary conditions to solve
for the constants of integration. The standard sign
convention for beams is that the internal bending
moment is positive when it acts to make the beam
vec
?
M(x) =
concave up.
Consider a cantilever beam with span L = 3 m that
has a point force P = 15 kN and couple moment
Mo = 8 kN - m applied at the free end, as shown.
(Figure 1)The beam has E = 200 GPa and I =
5x104 cm
Submit
Part B - The elastic curve
Let x represent the distance from the free end of the beam. Write the equation for the elastic curve for the beam.
Express your answer so the deflection is in mm when æ is in m.
• View Available Hint(s)
Figure
1 of 1>
V ΑΣφ
?
vec
P
v(x) =
Submit](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed59431e-03fe-4a4d-a12d-387ad46dfe48%2F37d20da3-64ba-4638-85b1-ac7b8240b8ab%2F083hm5i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Learning Goal:
To use integration to find the equation for the elastic
curve of a beam.
Part A - The moment function
For beams with small deflections, the shape of the
elastic curve is related to the internal bending
d?v
moment by the equation EI = M(x), where
da?
x is the position along the beam as measured from
the free end of the beam, v is the transverse
Let x represent the distance from the free end of the beam. Write the moment function in terms of x using the standard sign convention for beams.
Express your answer so the moment is in kN. m when r is in m.
displacement, E is the elastic modulus of the
• View Available Hint(s)
material, and I is the moment of inertia for the
section. The equation for the elastic curve can be
determined by integrating this equation twice with
respect to x and using boundary conditions to solve
for the constants of integration. The standard sign
convention for beams is that the internal bending
moment is positive when it acts to make the beam
vec
?
M(x) =
concave up.
Consider a cantilever beam with span L = 3 m that
has a point force P = 15 kN and couple moment
Mo = 8 kN - m applied at the free end, as shown.
(Figure 1)The beam has E = 200 GPa and I =
5x104 cm
Submit
Part B - The elastic curve
Let x represent the distance from the free end of the beam. Write the equation for the elastic curve for the beam.
Express your answer so the deflection is in mm when æ is in m.
• View Available Hint(s)
Figure
1 of 1>
V ΑΣφ
?
vec
P
v(x) =
Submit
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