Chrome File Edit View History Bookmarks People Window Help 6

Chrome File Edit View History Bookmarks People Window Help 6 0:52 89% GJ: Thu Jul 5 14:05 Q FTU Login-Canvas ?MasteringEngineering Master Chrome File Edit View History ? × CSecure https://session.masteringengineering.com/myct/itemView?assignmentProblemiD-7376996&offset-next; Structural Analysis Naser «Homework 6 Problem 7.36 7 of 7 Consider the beam shown in (Figure 1). EI is constant. Assume that EI is in kN-m2. Suppose that M = 70 kN·m. Use the moment-area theorems to solve this problem. Follow the sign convention. Part A Select the correct formulations of moment-area theorems Check all that apply. Points. The change in slope between any two points on the elastic curve equals the area under the M/EI diagram between these two The vertical deviation of the tangent at a point (A) on the elastic curve with respect to the tangent extended from another point Figure 1 of 1 (B) equals the moment of the area under the M/EI diagram between the two points (A and B). This moment is calculated about point A, where the deviation tA/B is to be determined. The vertical deviation of the tangent at a point (A) on the elastic curve with respect to the tangent extended from another point (B) equals the moment of the area under the M/EI diagram between the two points (A and B). This moment is calculated about point B, where the deviation tByA is to be determined. The change in slope between any two points on the elastic curve equals a half the area under the M/EI diagram between these two points. 3 m 3 m 3 mm Submit st Ans Part B Complete previous part(s)

Solution

Moment Area Theorem

1. First Moment Area Theorem

The difference of slope between any two points on a continuous elastic curve of a beam is equal to the area under the M / EI curve between these points.

2. Second Moment Area Theorem

The vertical distance (tangential deviation) of any point A on the elastic curve of a beam from a tangent drawn at any other point B on the elastic curve equals the first moment, with respect to an axis at A, of the area under the M/(EI) diagram between ordinates at A and B.

Therefore option (1) and (2) are correct.