Elastic deflections Flashcards
What happens when a beam is subjected to two-point loads?
Will deflect
Beams subjected to bending will be accompanied by what?
- A deflection, u
- A rotation, θ
How is θ measured?
From the horizontal axis
How can flexural stiffness be determined?
E*I
How can you calculate radius of curvature?
EI/M
How can rotation θ be calculated?
θ ≈ du/dx = ∫M/EI *dx
How can we obtain the vertial deflection?
Integrate rotation
What is a sagging moment know as?
A positive moment
What is a hogging moment known as?
“negative” moment
What is a downward deflection known as?
“negative” deflection
What is a upward deflection known as?
“positive” deflection
What is a downward rotation known as?
“negative” slope
What is an upward rotation known as?
“positive” slope
What are boundary conditions?
Locations in the beam where the slope and deflection are known
When are Macaulays brackets used?
Macaulay brackets are special expressions that are denoted using square brackets for expressions beyond x
What happens if the value in the Macaulay bracket is negative?
When the equation within the bracket results in a negative value, the whole bracket is set to a value of zero and ignored
