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Drawing SFD and BMD with Summation Method: Engineering Fundamentals

Learn to draw Shear Force Diagram (SFD) and Bending Moment Diagram (BMD) using the summation method. Understand key concepts like shear and moment changes between points, and the impact of concentrated loads on diagrams. Practice with example calculations.

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Drawing SFD and BMD with Summation Method: Engineering Fundamentals

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  1. Lecture No. 16 Drawing SFD and BMD Objective: To be able to drawn SFD and BMD using summation method.

  2. Notes To Remember When Drawing SFD and BMD • 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). • 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). • 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.

  3. Notes To Remember When Drawing SFD and BMD • (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. • 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.

  4. 20N 3N/m 2N/m 40N/m 20N 3N/m 2N/m STEP (1) Reaction 40N/m 5m 2m 3m 2m 3m 16.23 18.3 8.3 8.3 Shear + 11.7 16.23 2nd. Degree curve 83.1 Moment 68 66.5 43.1 2nd. Degree curve 3rd. Degree curve 44.6 + +

  5. Drawing V and M 9 6 6 V(x) 18N + Shear force diagram -1 4.9m M(x) 58.8N-m 54N-m Bending moment diagram + Remark: ● points of zero shear correspond to maximum moment. ● locations of zero shear and maximum moment are important to indicate on the diagram

  6. 10N 10N 2N/m A B 1m 10N 1m 1m 2m 2m 2m 4m 10N 10N-m B 10N A 10N 10N-m

  7. 10N 10N-m 20N 10N 10N 10N-m 5.67 12.33N 12.33N 2.33 S.F.D 1.2 5.67 5.67 B.M.D.

  8. Convex 37.7 31.7 N. 31.7 – 50 = 18.3 -18.1 – 6 = 24.7 26.3 S. F. D. 26.3 convex convex 107.1 St. Line 3rd. day 65.5 64.5 N·m 13 B. M.D.

  9. The enD

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