Stiffness factor for member in beam

In summary: I have not noticed an actual definition of "far end" but just thinking about how I would expect a beam to behave it is clear that if any part of a beam is unable to rotate at all it will make the beam stiffer at all joints.
  • #1
fonseh
529
2

Homework Statement


In this question , I don't understand why the KBC is 4EI / L ...

Homework Equations

The Attempt at a Solution


I was told that for the far end pinned or roller supported , the K = 3EI / L , so shouldn't the KBC = 3EI / L.. Is the author wrong ?

In the 3rd photo , we can see that for far end pinned supported , k = 3EI / L , not 4EI / L
 

Attachments

  • P861M.png
    P861M.png
    37.6 KB · Views: 727
  • vRd8Z.png
    vRd8Z.png
    45.2 KB · Views: 590
Last edited:
Physics news on Phys.org
  • #2
fonseh said:
for the far end pinned or roller supported , the K = 3EI / L , so shouldn't the KBC = 3EI / L.. Is the author wrong ?
BC is only a segment of the beam ABCD. The "far end" of BC from B is D.
Think about it: if D were just a pin then the beam could rotate a bit about D, allowing it equally to rotate a little about C. But with D fixed, it is much harder for there to be any rotation about C.
 
  • Like
Likes fonseh
  • #3
haruspex said:
BC is only a segment of the beam ABCD. The "far end" of BC from B is D.
Think about it: if D were just a pin then the beam could rotate a bit about D, allowing it equally to rotate a little about C. But with D fixed, it is much harder for there to be any rotation about C.
So , in this problem , the far end of AB is D , as D s pinned , so the KAB is 3EI / L ? If D is fixed , then KAB would be 4EI / L ?
 

Attachments

  • 583.png
    583.png
    80.5 KB · Views: 1,575
  • #4
fonseh said:
So , in this problem , the far end of AB is D , as D s pinned , so the KAB is 3EI / L ? If D is fixed , then KAB would be 4EI / L ?
That's my understanding. But please bear in mind that my entire knowledge of the subject comes from the textbook extracts you have posted.
 
  • #5
haruspex said:
That's my understanding. But please bear in mind that my entire knowledge of the subject comes from the textbook extracts you have posted.
May I know which part ? Can you highlighted it ?
 
  • #6
fonseh said:
May I know which part ? Can you highlighted it ?
I have not noticed an actual definition of "far end" but just thinking about how I would expect a beam to behave it is clear that if any part of a beam is unable to rotate at all it will make the beam stiffer at all joints. Hence that is how I interpret the term.
 
  • Like
Likes fonseh

What is the stiffness factor for a member in a beam?

The stiffness factor for a member in a beam is a measure of its resistance to deformation under an applied load. It is typically represented by the symbol EI, where E is the modulus of elasticity and I is the moment of inertia of the member.

How is the stiffness factor calculated?

The stiffness factor for a member in a beam is calculated by multiplying the modulus of elasticity (E) of the material by the moment of inertia (I) of the member. The formula is EI = E x I. The resulting unit for stiffness factor is force multiplied by length squared (kN.m2 or lb.in2).

What is the significance of the stiffness factor in beam design?

The stiffness factor is an important parameter in beam design because it determines how much a beam will bend or deflect under a given load. A higher stiffness factor indicates a stiffer and stronger beam, while a lower stiffness factor may result in excessive deflection or failure of the beam.

How does the stiffness factor affect the overall behavior of a beam structure?

The stiffness factor plays a crucial role in determining the overall behavior of a beam structure. It affects the deflection, bending moment, and shear forces experienced by the beam, as well as its ability to support loads and resist external forces. A higher stiffness factor results in a more rigid and stable structure, while a lower stiffness factor may lead to excessive movement and potential failure.

What factors can influence the stiffness factor of a member in a beam?

The stiffness factor of a member in a beam can be influenced by several factors, including the material properties, cross-sectional shape and size of the member, and the type and magnitude of the applied load. Additionally, boundary conditions and supports can also affect the stiffness factor of a beam member.

Similar threads

Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
2
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
9
Views
3K
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
31
Views
3K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
9K
  • Introductory Physics Homework Help
Replies
9
Views
2K
Back
Top