Dr. Ali H. Al-Gadhib 1 Lecture No. 16 To be able to drawn SFD and BMD using summation method.

Dr. Ali H. Al-Gadhib 2 (1) The change of shear between two points A and B is equal to the area of the loading between A and B. Or (The shear at point B is equal to the shear at point A + the area of load between A and B). (2) The change of moment between two points A and B is equal to the area of shear diagram between A and B. Or (The moment at point B is equal to the moment at point A + the area of shear between A and B). (3) The shear is changed by the magnitude of the concentrated load. Upward load increase shears by its magnitude whereas downward load decrease shears by its magnitude. Notes To Remember When Drawing SFD and BMD

Dr. Ali H. Al-Gadhib 3 (4) Concentrated moment does not affect the value of shear but increases moment by its magnitude if the applied moment is clockwise and decrease moment by its magnitude if it is applied counterclockwise. (5) The moment is maximum wherever shear changes its sign. Both magnitude and location of max. moment are important to be shown on the bending moment diagram. Notes To Remember When Drawing SFD and BMD

Dr. Ali H. Al-Gadhib 4 20N 3N/m 2N/m 40N/m 20N 3N/m 2N/m 40N/m m 2m 3m 2m 3m STEP (1) Reaction nd. Degree curve + Shear 3 rd. Degree curve nd. Degree curve + + Moment

Dr. Ali H. Al-Gadhib V(x)V(x) 4.9m + 18N Shear force diagram Bending moment diagram + 54N-m 58.8N-m M(x)M(x) Remark: ● points of zero shear correspond to maximum moment. ● locations of zero shear and maximum moment are important to indicate on the diagram

Dr. Ali H. Al-Gadhib 6 A B 10N 2N/m 2m 1m 4m 2m 10N 10N-m 10N A B

Dr. Ali H. Al-Gadhib 7 20N 10N 10N-m 12.33N 5.67 S.F.D 12.33N B.M.D.

Dr. Ali H. Al-Gadhib 8

Convex 31.7 N – 50 = 18.3 S. F. D – 6 = N·m B. M.D rd. day convex St. Line

Dr. Ali H. Al-Gadhib 10