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singularity functions

# 3 lecture 16 beams deformation by singularity

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Unformatted text preview: 2 ) (15b) Slide No. 3 LECTURE 16. BEAMS: DEFORMATION BY SINGULARITY FUNCTIONS (9.5 – 9.6) Singularity Functions Introduction Figure 9 y ENES 220 ©Assakkaf P w x y L/4 L/2 w L x L (a) (b) 2 Slide No. 4 LECTURE 16. BEAMS: DEFORMATION BY SINGULARITY FUNCTIONS (9.5 – 9.6) Singularity Functions ENES 220 ©Assakkaf Introduction – While for the beam of Figure 9b, the shear V or moment M cannot be expressed in a single analytical function. In fact, they should be represented for the three intervals, namely 0 ≤ x ≤ L/4, L/4 ≤ x ≤ L/2, and L/2 ≤ x ≤ L Slide No. 5 LECTURE 16. BEAMS: DEFORMATION BY SINGULARITY FUNCTIONS (9.5 – 9.6) Singularity Functions ENES 220 ©Assakkaf Introduction – For the three intervals, the shear V and the bending moment M can are given, respectively, by y P w wL P+ for 0 ≤ x ≤ L / 4 2 wL V ( x) = for L/4 ≤ x ≤ L / 2 2 wL − w x − L for L / 2 ≤ x ≤ L 2 2 x L/4 L/2 L 3 Slide No. 6 LECTURE 16. BEAMS: DEFORMATION BY SINGULARITY FUNCTIONS (9.5 – 9.6) Singularity Functions Introduction y and ENES 220 ©Assakkaf P w x L/4 L/2 L PL 3wL2 wL − + Px + x − 4 8 2 3wL2 wL M ( x) = − + x 8 2 2 2 w L 3wL wL − + x− x− 8 2 2 2 for 0 ≤ x ≤ L /...
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