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# Lecture5a(1)

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### Lecture5a(1)

1. 1. Today: Internal effects in beams Book: Chapter 7.1-7.3 + hand outs on Blackboard
2. 2. A C B Calculate the internal forces in C.
3. 3. Name convention A cutting plane is positive when the perpendicular coordinate axis (e.g. the x-axis) is pointing outward.
4. 4. Sign convention Normal and shear forces are positive when they are acting on a positive cutting-plane in the positive x- or y-direction, or when it is acting on a negative cutting-plane in the negative direction. A bending moment is positive when it gives rise to a tensile stress in the side of the beam on the positive z-direction.
5. 5. Sign convention Positive section plane
6. 6. Interaction
7. 7. Normal stress Shear stresses
8. 8. Sign convention A stress component is positive when it is acting on a positive cutting-plane in the positive direction, or when it is acting on a negative cutting-plane in the negative direction. A stress component is negative otherwise.
9. 9. Note: the stresses are drawn in their positive directions. xzσ
10. 10. Interaction force in two-dimensional calculations Normal force N Shear force Vz = V Bending moment My = M
11. 11. A B Determine the shear force and moment diagram of the cantilever beam. (Determine the interaction force V and M for every position x on the beam).
12. 12. A D B Determine the shear force and moment diagram of this structure. C
13. 13. Determine the shear force and moment diagram of the wing of this airplane.
14. 14. Determine the normal force diagram in the bar with length L, cross-section A and density ρ due its own weight. Bonus: The column is made of steel, ρ=7800 kg/m3 with an ultimate stress σu=400 MPa. For what length L will the beam fail due to its own weight?