θB/A refers to:-
Explanation: In the above given equation, if A is first point and B is second, then θB/A is the LHS.
If area of M/EI diagram between points A and B is –ve, then angle from tangent A to tangent B will be measured :-
Explanation: Standard sign convention is applied everywhere in the proof, so it is quite obvious.
What is the dimension of θB/A if area is measured in SI unit:-
Explanation: Since area is measured in SI units, result too will be in Si units.
The vertical deviation is measured along (if first point is A and second point is B):-
This makes the integration much easier during calculation of deflection.
he vertical deviation of tangent at point say A on the elastic curve with respect to the tangent extended from another point say B equals the “moment” of the area under the M/EI diagram between the two points about point :-
Explanation: Since, we are taking A as origin.
–ve M/EI area means tangent at A is:-
Explanation: Since, during derivation we have always assumed upward to be positive.
In general tA/B implies:-
Explanation: It is just a standard to differentiate between tA/B and tB/A.
TA/B and tB/A are:-
Explanation: In one case, we will take moment about point A while in other case moment is taken about point B. So, it can be anything.
The change in slope between any two points on the elastic curve equals the area of M/EI diagram between both end points of beam.
State whether the above statement is true or false.
Explanation: Change in slope will be equal to area of M/EI diagram between those two points.
–ve moment bends the beam convex down.
State whether the above sentence is true or false.
Explanation: -ve moment bends a beam concave down.