Question
1. Equilibrium equations.
2. Force-temperature-deformation relationships.
3. Compatibility equations.
Two uniform, linearly elastic members are joined togetherat B, and the resulting two-segment rod is attachedto a rigid support at end A. When there is no load onthe 2-element bar (i.e., when P = 0) there is agap of delta bar =0.2 mm between the end of element (2) and the rigid wallat C. Element (1) is steel withmodulus E1 = 210 GPa, cross-sectionalarea A1 = 700 mm2, andlength L1 = 2.1 m; element (2) istitanium alloy with E2 = 120GPa, A2 = 1000mm2, and L2 = 1.8 m.A single external force P =80 kN is applied at node B. (a) Determine the axialstresses ?1 and ?2 inducedin the respective rod elements when theload P is applied. (Use plus for tension andminus for compression.) ?1 = MPa ?2 = MPa (b) Determine the correspondingdisplacement uB of thejoint B. uB = mm This problem is a staticallyindeterminate problem that involves misfits and, in a few cases,temperature change. Solve these problems by writing appropriateequations of each of the following three fundamental types: 1. Equilibrium equations. 2. Force-temperature-deformation relationships. 3. Compatibility equations. Use the Basic Force Method to solvethese simultaneous equations.
Explanation / Answer
HI i will throw some light on it I dont assure u it will work Here we go When the load p is applied initially there will be no stressor change in length in element (2) until the element (1)is displaced by 0.2 mm But when element (1) is left free to expand its L wouldbe L1=Pl1/A1E1 but it is more than 0.2mm hence the restricted change in length would then cause stressin element (2) that restricted change in length in element (1) is equalto change in length in element (2) L2 = L1-0.2
