Finding Internal Loadings on a Cantilevered Beam

[newbphysic]

Determine the resultant internal loadings acting on the cross section
at C of the cantilevered beam
http://imgur.com/Q4ZUTOq
1. Homework Statement
F = 270 N/m

Homework Equations

ΣV = 0
ΣM = 0
ΣN = 0

The Attempt at a Solution

section CB[/B]

k/6 = 270/9
k = 180 N/m
resultant force = area under the curve = 1/2 * 180 * 6 = 540 N

ΣN = 0
-N = 0
N = 0

ΣV = 0
V - resultant = 0
v = resultant = 540 N

How can i find M ?

 

[SteamKing]

Determine the resultant internal loadings acting on the cross section
at C of the cantilevered beam
http://imgur.com/Q4ZUTOq
1. Homework Statement
F = 270 N/m

Homework Equations

ΣV = 0
ΣM = 0
ΣN = 0

The Attempt at a Solution

section CB[/B]

k/6 = 270/9
k = 180 N/m
resultant force = area under the curve = 1/2 * 180 * 6 = 540 N

ΣN = 0
-N = 0
N = 0

ΣV = 0
V - resultant = 0
v = resultant = 540 N

How can i find M ?

You can calculate the shear force diagram for this beam given the loading as shown.

What's the relationship between the bending moment and the shear force?

 

[PhanthomJay]

You have already determined the resultant force of the load . At what point does it act? Then sum moments and watch directions.

 

[newbphysic]

You can calculate the shear force diagram for this beam given the loading as shown.

What's the relationship between the bending moment and the shear force?

both occur because of force perpendicular to beam ?

You have already determined the resultant force of the load . At what point does it act? Then sum moments and watch directions.

center of the beam ?

 

[SteamKing]

both occur because of force perpendicular to beam ?

That's not the relationship which is useful in calculating M.

At the free end of the cantilever, M = 0. What must M be at point C for that segment of the beam to remain in equilibrium?

 

[PhanthomJay]

[QUOTE="newbphysic, post: 5400435, member: 557120]center of the beam ?[/QUOTE] in the free body diagram you have drawn, the resultant of the triangularity distributed load acts at the cg of that load. Where's that?

 

[newbphysic]

That's not the relationship which is useful in calculating M.

At the free end of the cantilever, M = 0. What must M be at point C for that segment of the beam to remain in equilibrium?

the relationship between M and shear force is shear force causes bending moment ?

Since M=0 at the end of cantilever that means M must be 0 at C to remain equilibrium

center of the beam ? in the free body diagram you have drawn, the resultant of the triangularity distributed load acts at the cg of that load. Where's that?

if the beam is uniform then cg will be length / 2 = 6/2 = 3m from C

 

[SteamKing]

the relationship between M and shear force is shear force causes bending moment ?

Since M=0 at the end of cantilever that means M must be 0 at C to remain equilibrium

The only problem is, M can't be zero at point C, 'cuz of that applied force. What's the moment due to the applied force?

 

[PhanthomJay]

if the beam is uniform then cg will be length / 2 = 6/2 = 3m from C

in your diagram, the loading on the beam is not uniform; it is triangular. The centroid of a triangle is not at its center.

 

[newbphysic]

The only problem is, M can't be zero at point C, 'cuz of that applied force. What's the moment due to the applied force?

The moment is the sum of all forces from B to C = 540 N

in your diagram, the loading on the beam is not uniform; it is triangular. The centroid of a triangle is not at its center.

centroid of triangle is 1/3 * 6 = 2

 

[SteamKing]

The moment is the sum of all forces from B to C = 540 N

That's not what a moment is.

centroid of triangle is 1/3 * 6 = 2

How do you use the centroid of the applied load to calculate the moment due to that load?

 

[PhanthomJay]

centroid of triangle is 1/3 * 6 = 2

Yes , 2 m from where? Now place the resultant force at that point and sum moments about the left end of your section to find the internal moment at that end.

 

[newbphysic]

That's not what a moment is.

moment is force times distance.
so it's 540 times the distance to the left side of the beam
Is that what you mean ?

How do you use the centroid of the applied load to calculate the moment due to that load?

total force times the distance from centroid to C

Yes , 2 m from where? Now place the resultant force at that point and sum moments about the left end of your section to find the internal moment at that end.

2m from zero reference point means from the left of the beam.
so moment = $force * distance = 540 *2 = 1080 Nm$

$ΣM = 0$

$M + 1080 Nm = 0$

$M = -1080 Nm$

 

[PhanthomJay]

2m from zero reference point means from the left of the beam.
so moment = $force * distance = 540 *2 = 1080 Nm$

$ΣM = 0$

$M + 1080 Nm = 0$

$M = -1080 Nm$

Yes, but can you explain the meaning of the minus sign in front of your answer?

 

[newbphysic]

Yes, but can you explain the meaning of the minus sign in front of your answer?

M is anti - clockwise

Thanks a lot phantom

 

[PhanthomJay]

M is anti - clockwise

Thanks a lot phantom

OK!