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Beam Analysis

Beam Analysis. We require from buildings two kinds of goodness: first, the doing their practical duty well: then that they be graceful and pleasing in doing it. -John Ruskin. Beam. Structural member that carries a load that is applied transverse to its length Used in floors and roofs

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Beam Analysis

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  1. Beam Analysis We require from buildings two kinds of goodness: first, the doing their practical duty well: then that they be graceful and pleasing in doing it. -John Ruskin

  2. Beam • Structural member that carries a load that is applied transverse to its length • Used in floors and roofs • May be called floor joists, stringers, floor beams, or girders

  3. Chasing the Load • The loads are initially applied to a building surface (floor or roof). • Loads are transferred to beams which transfer the load to another building component. Girder Beam Girder Beam

  4. Static Equilibrium • The state of an object in which the forces counteract each other so that the object remains stationary • A beam must be in static equilibrium to successfully carry loads

  5. Static Equilibrium • The loads applied to the beam (from the roof or floor) must be resisted by forces from the beam supports. • The resisting forces are called reaction forces. Applied Load Reaction Force Reaction Force

  6. Reaction Forces • Reaction forces can be linear or rotational. • A linear reaction is often called a shear reaction (F or R). • A rotational reaction is often called a moment reaction (M). • The reaction forces must balance the applied forces.

  7. Beam Supports The method of support dictates the types of reaction forces from the supporting members.

  8. Beam Types Simple Continuous Cantilever Moment (fixed at one end)

  9. Beam Types Fixed Moments at each end Propped – Fixed at one end; supported at other Overhang

  10. Simple Beams Applied Load BEAM DIAGRAM Applied Load FREE BODY DIAGRAM Note: When there is no applied horizontal load, you may ignore the horizontal reaction at the pinned connection.

  11. Fundamental Principles of Equilibrium Fy = 0 The sum of all vertical forces acting on a body must equal zero. Fx = 0 The sum of all horizontal forces acting on a body must equal zero. Mp = 0 The sum of all moments (about any point) acting on a body must equal zero.

  12. Moment • A moment is created when a force tends to rotate an object. • The magnitude of the moment is equal to the force times the perpendicular distance to the force (moment arm). F M

  13. Calculating Reaction Forces Sketch a beam diagram.

  14. Calculating Reaction Forces Sketch a free body diagram.

  15. Calculating Reaction Forces Use the equilibrium equations to find the magnitude of the reaction forces. • Horizontal Forces • Assume to the right is positive +

  16. Calculating Reaction Forces • Vertical Forces • Assume up is positive + Equivalent Concentrated Load Equivalent Concentrated Load

  17. Calculating Reaction Forces • Moments • Assume counter clockwise rotation is positive + A B 0 = = 7700 lb

  18. Calculating Reaction Forces • Now that we know , we can use the previous equation to find . 0 = = 7700 lb 9300 lb =

  19. Shear Diagram Shear at a point along the beam is equal to the reactions (upward) minus the applied loads (downward) to the left of that point. 0 = = 7700 lb 9300 lb =

  20. Moment Diagram Kink in moment curve

  21. Moment Diagram 4000 lb M P 2.15’ 0 = 9300 lb =

  22. Moment Diagram

  23. Moment Diagram A B C = 2.15 ft

  24. Beam Analysis • Example : simple beam with a uniform load, w1= 1090 lb/ft • Span = 18 feet Test your understanding: Draw the shear and moment diagrams for this beam and loading condition.

  25. Shear and Moment Diagrams Shear Moment Max. Moment = 44,145l ft-lb Max. Shear = 9,810 lb

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