Chapter 8 - Deflections

Semester Overview Chapter Topic 1 terminology 2-5 statics review 6 influence lines 8-9 deflections 10-12 indeterminate structures   Quiz 3 Topics Deflections and Slopes 1. Integration / Superposition (deflection tables)    beams 2. Conjugate Beams 3. Virtual Work beams, trusses, frames Deflection in Wood Structures Beam Design IBC deflection limits homework: 6.14, 18, 22 Semester Project sample house load and deflection calcs Structural Biomimetics Grown Buildings Intro to 322 Silk Dome Curved Roof Ridge due to Differential Settlement Hobbit House ridge framing finished ridges Sagging Framing - see diagram at bottom of page Sagging Roof 1 Sagging Roof 2 Quiz 4 & 5 Topics Forces and Moments in Indeterminate Structures 1. Integration / Superposition Quiz 4    beams, trusses, frames 2. Conjugate Beams Quiz 4 3. Virtual Work Quiz 4 4. Slope-Deflection Quiz 4 5. Moment-Distribution Quiz 5

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Objectives Visualize the shape of a beam's elastic curve. Calculate the slope and deflection at various locations in a beam using the elastic-curve equation. State the boundary, continuity and symmetry conditions. Derive the elastic-curve equation. Determine the distributed-load or moment function. Integrate to determine the slope and elastic-curve functions. Derive four indefinite integrals if starting with the distributed-load function. Derive two indefinite integrals if starting with the moment function. Solve for the integration constants. Calculate the slope and deflection at various locations in a beam using the conjugate-beam method. Determine the ground reactions on the real beam. Draw the shear-force and bending-moment diagrams for the real beam. Convert the real beam into its conjugate. Load the conjugate beam with a distributed load having the same shape as M on the real beam divided by EI. Draw the shear-force and bending-moment diagrams for the conjugate beam, or cut the conjugate beam at the desired location and determine V' and M' using equilibrium. Convert the conjugate-beam information back to the real beam.  (V' = θ, M' = v)

Concepts   1.  deflection diagrams and the elastic curve 2.  elastic-beam theory 3.  the double integration method  - ce 110 statically-determinate deflection notes  - ce 110 statically-indeterminate deflection notes  - ce 110 deflection formulas  - mecmovies 4.  moment-area theorems 5.  conjugate-beam method

Problems   * examples to be discussed in class 7e Examples 7e Homework Autodesk Robot integration method     08.001 -- -- solution solution   08.002 -- -- -- --   08.003 -- -- -- solution   08.004 -- -- solution --   08.005 -- -- solution --   08.006 -- solution*3 -- --   08.007 -- -- -- solution   08.008 strategy solution*1 -- --   08.009 -- solution*2 -- -- moment -area method   08.010 strategy solution*1 -- --   08.011  --  -- -- --   08.012  --  -- -- --   08.013  --  -- -- solution   08.014  --  -- -- solution   08.015  --  -- -- --   08.016  --  -- -- --   08.017  --  -- -- --   08.018 -- solution*4 -- --   08.019  --  -- -- --     08.020    --    --   --   --       08.021   --   solution*2   --   --       08.022    --    --   --   --       08.023    --    --   --   --       08.024    --    --   --   --       08.025   --   solution*5   --   solution       08.026    --    --   --   --       08.027   --   solution*3   --   --     conjugate -beam method   08.028   --   --   solution   --       08.029   --   --   solution   solution       08.030   --   --   solution   --       08.031   --   --   --   --       08.032   --   --   --   solution       08.033   --   --   --   solution       08.034   --   --   --   --       08.035   --   --   solution   --       08.036   --   --   solution   solution       08.037   --   --   --   --       08.038   --   --   solution   --