Chapter 5 - Axial Deformation

Objectives Course objective:  To understand the stress-strain and load-displacement relationships for axial force members. Learning objectives: Apply concepts from chapters 1-4 to axially-loaded members. Sum forces (1.17). Sum moments (1.18). Calculate deformations of axially-loaded members using force-displacement relationship (1.36 when no statics is involved; 1.03 when statics is involved). Identify statically indeterminate axially-loaded members from statically determinate axially-loaded members. Derive the compatibility relationship for coaxial (0.74), end-to-end (0.75), and rotating rigid (0.63) components. Judge whether a modification of the basic compatibility relationship is necessary in order to deal with gaps, opposing members, and floating (no ground pin in rotating rigid bar) members in the structure (0.54). Calculate free (no stress) thermal deformations (0.83). Derive the compatibility relationship for coaxial (0.47), end-to-end (0.51), and rotating rigid components with temperature changes. Judge whether a modification of the basic compatibility relationship is necessary in order to deal with gaps, opposing members, and floating (no ground pin in rotating rigid bar) members in the structure with temperature changes. 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  (17 minutes) 1. axial members video notes 2. statically-indeterminate structures video notes 3. homework solution steps video notes 4. algebra help     - solving for one variable in one equation (first 2 min.)     - solving for multiple variables in multiple equations

Demos  (11 minutes) 1. axial deformation video 2. compression failures video

Quiz Prep 1. The problems in chapters 4 and 5 take longer to complete than those in chapters 1-3, so the second quiz usually has fewer calculation questions.   Unfortunately, having fewer questions means at least some of them will be worth more points. 2. The quiz will have more emphasis on chapter 5 than chapter 4, since more homework was assigned from chapter 5. 3.  The format will be the same as the first quiz.

Problems  (99 minutes) assigned 3e 2e 1e aids WP format axial yes 05.001 05.001* 05.001 strategy solution TENU -- 05.002 05.002* 05.002 -- -- TENU yes 05.003 05.003* 05.003 video solution TENU -- -- 05.004* 05.004 strategy solution TENU B30     --   05.004   --   --   --   --   --   -- 05.005 05.005* 05.005 -- -- TENU -- 05.006 05.006* 05.006 -- solution -- yes 05.007 05.007 05.007 video solution TENU yes 05.008 05.008* 05.008 strategy solution GO -- 05.009 05.009* 05.009 strategy solution TENU -- 05.010 05.010 05.010 -- solution TENU     --   05.011   05.011   05.011 -- -- --   -- 05.012 05.012 --   --   --   -- -- -- -- 05.012 -- -- -- -- 05.013 05.013 05.013 -- -- TENU     --   05.014   --   --   --   --   TENU   multiple bars yes -- 05.014* 05.014 video solution TENU B31 yes 05.015 05.015* 05.015 strategy solution TENU yes 05.016 05.016* 05.016 video solution TENU -- 05.017 05.017* 05.017 strategy solution GO -- -- 05.018* 05.018 -- -- --     yes   05.018   --   --   --   solution   TENU   -- 05.019 05.019 05.019 -- solution TENU -- -- 05.020 05.020 -- -- --     --   05.020   --   --   --   --   TENU   -- 05.021* 05.021 05.021 strategy solution -- -- 05.022 05.022 05.022 strategy solution -- indeterminate yes 05.023 05.023 05.023 video solution GO -- 05.024 05.024* 05.024 -- solution TENU -- 05.025 05.025* 05.025 -- -- -- yes -- 05.026* 05.026 video solution TENU B32     --   05.026   --   --   --   --   TENU   yes 05.027 05.027* 05.027 strategy solution TENU -- 05.028 05.028 05.028 -- solution TENU -- 05.029 05.029 05.029 strategy solution -- -- 05.030 05.030* 05.030 strategy solution TENU -- 05.031 05.031 05.031 -- -- TENU yes 05.032 05.032* 05.032 video solution TENU -- -- 05.033* 05.033 -- -- -- yes -- 05.034* 05.034 video solution TENU B33 -- -- 05.035* 05.035  -- solution -- -- -- 05.036* 05.036 strategy solution TENU B34     --   05.033   --   --   --   --   TENU       --   05.034   --   --   --   --   --       --   05.035   --   --   --   --   TENU       --   05.036   --   --   --   --   TENU   -- -- 05.037* 05.037 -- -- TENU B35 -- -- 05.038* 05.038 strategy solution TENU B36 -- -- 05.039 05.039 -- -- --     --   05.037   --   --   --   --   --       --   05.038   --   --   --   --   --       --   05.039   --   --   --   --   TENU       --   05.040   --   --   --   --   --       --   05.041   --   --   --   --   TENU       --   05.042   --   --   --   --   --       --   05.043   --   --   --   --   --   -- 05.044 05.040* 05.040 strategy solution TENU yes 05.045 05.041* 05.041 video solution TENU     --   05.046   --   --   --   --   --       --   05.047   --   --   --   --   GO   -- 05.048 05.042 05.042 -- solution GO yes -- 05.043 05.043 strategy solution TENU B37   thermal   --   05.049   --   --   --   --   TENU   yes 05.050 05.044* 05.044 strategy solution TENU -- 05.051 05.045* 05.045 -- solution TENU -- 05.052 05.046* 05.046 -- -- TENU -- 05.053 05.047 05.047 -- -- TENU yes 05.054 05.048* 05.048 strategy solution TENU -- 05.055 05.049 05.049 strategy solution GO yes -- 05.050* 05.050 video solution TENU B43     --   --   --   05.051 -- -- --   -- -- 05.051 05.052 -- -- TENU B38     --   05.056   --   --   --   --   TENU       --   05.057   --   --   --   --   TENU   -- 05.058 05.052 --   -- -- TENU       --   05.059   05.053   --   -- -- TENU   -- -- 05.054 05.053 -- -- TENU B39     --   --   05.055   05.054 video solution --   yes 05.060 05.056 05.055 strategy solution TENU -- 05.061 05.057 05.056 strategy solution -- -- -- 05.058 --   -- -- TENU B44     --   05.062   --   --   --   --   TENU   -- 05.063 05.059 --   -- -- GO -- -- 05.060 --   -- -- TENU B40     --   05.064   --   --   --   --   TENU   -- 05.065 05.061 05.057 -- solution --     yes   --   05.062   05.058 strategy solution GO B41       yes   --   05.063   05.059 video solution GO B42       --   05.066   05.064   05.060 strategy solution --   yes 05.067 05.065 05.061 -- -- GO stress concentrations -- 05.068 05.066* 05.062 -- -- -- -- 05.069 05.067* 05.063 -- -- -- -- 05.070 05.068* 05.064 -- -- -- -- 05.071 05.069* 05.065 -- -- -- -- 05.072 05.070* 05.066 -- -- -- -- 05.073 05.071* 05.067 -- -- -- -- -- -- 05.068 -- -- --     --   05.074   05.072   --   -- -- --   -- 05.075 05.073* 05.069 -- -- -- * numbers changed between editions props

 

 

 

The answers for 5.15 in the second edition should be σ₁ = 158.7 MPa (C), σ₂ = 26 MPa (T), v_A = 1.190 mm (down) and P = 72.3 kN. 

Part (b) of problem 5.21 in the second edition and parts (c) and (d) of problem 5.22 will not be on the quiz.

Part (d) of problem 5.49 in the second edition will not be on the quiz.  But if you're curious, example problem 3.2 on pages 56-57 explains the approach that is needed to solve part (d).