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Lecture # 27

Lecture # 27. Macaulay Functions. Deflection of Beams and Shafts. Discontinuity Functions. w. a b c. w. w. a + b. x. M (x). Remember that the distributed loads can start anywhere but Should continue to the end of the beam; otherwise

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Lecture # 27

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  1. Lecture # 27 Macaulay Functions. Deflection of Beams and Shafts Discontinuity Functions.

  2. w a b c w w a + b x M(x) Remember that the distributed loads can start anywhere but Should continue to the end of the beam; otherwise It should be forced to go to the end.

  3. Example: Find the slope of the beam at support A. 3N/m 100N 2N/m 10N-m 60.2=R1 R2=52.3N 4m 2m 2m 2m 3m x M(x)

  4. +

  5. w A B L Using Singularity Functions to Determine Reactions of Statistically Indeterminate Problems: Example 1: Find reaction at support A.

  6. Unknowns: { C1, C2, Ay } Boundary Conditions Solving:

  7. P A B MA MB b a L RB RA Example 2: Find reactions at support A & B.

  8. Unknowns: { C1, C2, RA, MA } Boundary Conditions One can use equilibrium equations to find the remaining unknowns (RB & MB).

  9. The enD

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