# Stiffness factor of beam member

If I have a beam with the left end being "A" and it is fixed at that end and the right end being "B" with a roller support, would KAB=3EI/L??

• you need to define the load, and the position you need to find the stiffness factor. Apr 28, 2021 at 8:06
• I'm speaking in terms of the far end formula, I want to know if hypothetically for a member which is fixed at the left, "A" and pinned/roller at the right. "B" if the stiffness for KAB with A being the reference point is 3EI/L Apr 28, 2021 at 8:26

## 2 Answers

By definition, the bending stiffness $$"K"$$of a structural member is the moment that must be applied to an end of the member to cause a unit rotation ($$\theta = 1$$) of that end.

- For a beam with far end fixed,

Substituting $$\theta_{A} = 1$$, we get

$$K_{AB} = 4EI/L$$

- For a beam with far end pinned,

$$= 3EI/L(\theta_{A} - 0) + (0 - 0)$$

$$M_{AB} = (3EI/L)\theta_{A}$$

Substituting $$\theta_{A} = 1$$, we get

$$K_{AB} = 3EI/L$$

Update to address your comment:

The stiffness factor at the far end B, is going to be

$$K=\infty$$

No matter what force you put at the end (point B), point B will never move if its simply supported.

## Uniform load

Assuming that this is what you are asking (left B, right A)

then $$k = \frac{185 EI}{l^3}$$

This is at $$x= 0.4126 \;l$$

• No but I am intrigued as to how 185 if used in that formula, may I have a site for reference if possible? Apr 28, 2021 at 8:28
• The OP is asking about the stiffness in matrix operation such as the direct stiffness method.
– r13
Apr 28, 2021 at 16:29