Chapter 11 - Statically Indeterminate Beams
Objectives
Course objective: To learn to calculate the displacements for beams under various loading configurations.
Learning objectives:
- Apply loads to force deflection or slope to be zero at some point.
- simply-supported beams with deflection forced to be zero (0.96)
- cantilever beams with slope forced to be zero (1.10)
- Identify statically indeterminate beams from statically determinate beams.
- Identify boundary conditions for simply-supported and cantilever beams.
- Recognize how to divide overhung and doubly-overhung beams into equivalent combination of simply-supported and cantilever beams.
- Recognize how to release propped-cantilever, three-support, doubly-fixed, flexible-support and gapped-support beams.
- Derive the compatibility relationship.
- Acquire relevant formulas from beam-deflection tables.
- Calculate the ground reactions based on the superposition method and Newton's Laws.
- propped-cantilever beams (0.95)
- three-support beams (0.71)
- movable-support, simply-supported beams (0.63)
- movable-support, cantilever beams (0.94)
The values in orange represent quiz performance. One represents average. Values greater than one represent easier topics. Values less than one represent harder topics.
Concepts (7 minutes)
1. statically indeterminate beam deflections video notes 2. superposition for indeterminate beams video notes 3. algebra help - solving for one variable in one equation (first 2 min.) Quiz Prep
1. Please be careful with feet to inch conversions! Unfortunately, inconsistent units is a common reason people lose points on this quiz. 2. The beam deflection tables will be attached to the quiz. 3. Note that the deflection formulas are numbered. Some quiz questions may ask you to identify the formula(s) necessary to solve a particular problem. Some questions may ask how many formulas from the table are needed to solve the problem. 4. The following is an example of how the more challenging superposition problems (47 through 58) in chapter 10 can be asked in order to keep the derivations short. If these problems are included on the quiz, it is likely that only two or three questions similar to the following would be given for any particular picture.
- Given: picture from problem 10.52 (from first edition), E = 200 GPa, I = 95E6 mm^4
- Problem: Determine the deflection at point B caused by ONLY the 20 kN point load. Answer: 0.00281 m
- Problem: Determine the deflection at point C caused by ONLY the 20 kN point load. Answer: 0.00912 m
- Problem: Determine the deflection at point B caused by ONLY the 50 kN point load. Answer: -0.0228 m
- Problem: Determine the deflection at point C caused by ONLY the 50 kN point load. Answer: -0.110 m
- Problem: Determine the deflection at point B caused by ONLY the distributed loads. Answer: 0.0171 m
- Problem: Determine the deflection at point C caused by ONLY the distributed loads. Answer: 0.0791 m
- Problem: Determine the deflection at point B caused by ONLY the point loads. Answer: -0.020 m
- Problem: Determine the deflection at point C caused by ONLY the point loads. Answer: -0.101 m
Problems (63 minutes)
assigned 3e 2e 1e aids WP format integration 11.001 11.001 11.001 -- -- -- 11.002 11.002 11.002 -- -- -- 11.003 11.003 11.003 -- -- -- 11.004 11.004 11.004 -- -- -- 11.005 11.005 11.005 -- -- -- 11.006 11.006 11.006 -- -- -- 11.007 11.007 11.007 -- -- -- 11.008 11.008 11.008 -- -- -- 11.009 11.009 11.009 -- -- -- 11.010 11.010 11.010 -- -- -- 11.011 11.011 11.011 -- -- -- 11.012 11.012 11.012 -- -- -- 11.013 11.013 11.013 -- -- -- 11.014 11.014 11.014 -- -- -- 11.015 11.015 11.015 -- -- -- 11.016 11.016 11.016 -- -- -- 11.017 11.017 11.017 -- -- -- discontinuity
functions11.018 11.018 -- -- -- TENU 11.019 11.019 -- -- -- TENU 11.020 11.020 -- -- -- TENU 11.021 11.021 -- -- -- TENU 11.022 11.022 -- -- -- GO 11.023 11.023 -- -- -- GO 11.024 11.024 -- -- -- GO 11.025 11.025 -- -- -- -- 11.026 11.026 -- -- -- GO 11.027 11.027 -- -- -- -- superposition
with
non-flexible
supportsyes 11.028 11.028 11.018 video solution GO/GO yes 11.029 11.029 11.019 strategy solution TENU yes 11.030 11.030 11.020 video solution TENU 11.031 11.031 11.021 strategy solution -- 11.032 11.032 11.022 -- -- -- 11.033 11.033 11.023 -- -- -- 11.034 11.034 11.024 strategy solution -- 11.035 11.035 11.025 video solution -- 11.036 11.036 11.026 -- -- -- 11.037 11.037 11.027 -- -- -- 11.038 11.038 11.028 -- -- -- 11.039 11.039 11.029 -- -- -- 11.040 11.040 11.030 -- -- -- 11.041 11.041 11.031 -- -- -- 11.042 11.042 11.032 -- -- -- 11.043 11.043 11.033 -- -- -- 11.044 11.044 11.034 -- -- -- 11.045 11.045* 11.035 -- -- TENU yes 11.046 11.046* 11.036 strategy solution TENU yes 11.047 11.047* 11.037 strategy solution TENU yes 11.048 11.048* 11.038 video solution GO 11.049 11.049 11.039 -- -- TENU yes 11.050 11.050* 11.040 strategy solution GO 11.051 11.051 11.041 -- -- TENU yes 11.052 11.052 11.042 strategy solution TENU yes 11.053 11.053* 11.043 video solution TENU 11.054 11.054* 11.044 strategy solution TENU 11.055 11.055* 11.045 -- -- TENU 11.056 11.056 11.046 strategy solution TENU 11.057 11.057 11.047 -- -- TENU 11.058 11.058 11.048 -- -- TENU superposition
with
flexible
support11.059 11.059 11.049 strategy solution TENU 11.060 11.060 11.050 strategy solution TENU 11.061 11.061 11.051 -- -- -- yes 11.062 11.062 11.052 strategy solution TENU 11.063 11.063 11.053 -- -- TENU yes 11.064 11.064 11.054 video solution GO 11.065 11.065 11.055 -- -- TENU yes 11.066 11.066 11.056 strategy solution TENU 11.067 11.067 11.057 video solution -- yes 11.068 -- -- -- -- GO 11.069 -- -- -- -- -- 11.070 -- -- -- -- GO 11.071 -- -- -- -- -- 11.072 -- -- -- -- TENU 11.073 -- -- -- -- -- * numbers changed between first and second editions