Learning Goal: To solve for forces in statically indeterminate bars with axial loads. When the number of reaction forces is greater than the number of equilibrium equations, the system is statically indeterminate. Solving for the reactions requires some additional equations. These additional equations come from considering compatibility relationships (i.e., continuity of displacements and relationships between displacements and loads). For an axially loaded member, the compatibility relationship for the deflections can be written by setting the total relative axial displacement between the ends of the member to a known value. The load-displacement relationship & = Σ NL AE gives another equation for the deflections. Once the internal normal force of each segment is written in terms of the end reactions and applied loads, there is enough information to solve for the reactions. Figure Previous Figure C B F -L₂ < 1 of 2 > Figure A F X C B < 2 of 2 > Part A - Force with a known deflection The square bar shown (Figure 1) is 2.3 in. thick and 19 ft long and is fixed supported at both ends. A load directed leftward is applied at point C, as shown, L2 = 14 ft from the left end. The modulus of elasticity is E = 1.5×104 ksi .If point C moves 8 = 8×103 in. to the left, what is the applied force? Express your answer with appropriate units to three significant figures. ▸ View Available Hint(s) ΜΑ ? F = Value Units Submit Part B - Reaction with a known load Consider a new structure, where the thickness of the bar is reduced to 1.15 in. from C to B (it is still square) (Figure 2) and x = 14 ft. If the applied load is F= 105 kip, then what is the reaction at A? Let a positive reaction act to the right. The total length is still 19 ft. Express your answer with appropriate units to three significant figures. ▸ View Available Hint(s) HA FA = Value Units Submit ? Part C - Load point for equal forces Consider the structure from Part B (Figure 2). What value of a will lead to equal reaction forces at A and B? Express your answer in feet to three significant figures. ▸ View Available Hint(s) x = Submit ΜΕ ΑΣΦ vec ? ft