A system consists of two rigid end-plates to be tied together by three horizontal bars as shown in Fig. P6. Through a fabrication error, the central bar 2 is

0.0012m

shorter than bars 1 and 3 resulting in a gap,

\\\\Delta

.\ Develop the set of simultaneous equations needed to calculate the axial stress in each bar after the system has been mechanically pushed together a distance

\\\\Delta

, by some unknown force

F

, so that the gap is closed. Clearly draw all required FBDs. Explicitly count, as you write each equation, the number of unknowns and the number of equations. Put each useful equation in a "cloud". Do not solve or simplify the set of equations. Just show that you understand how to set up the equations and what known values would be substituted into each equation.\ For bars:\

E_(1)=E_(3)=210GPa\ E_(2)=70GPa\ L=0.3m\ A_(1)=A_(3)=2A_(2)=0.0004m^(2)

7. A system consists of two rigid end-plates to be tied together by three horizontal bars as shown in Fig. P6. Through a fabrication error, the central bar 2 is 0.0012m shorter than bars 1 and 3 resulting in a gap, . Develop the set of simultaneous equations needed to calculate the axial stress in each bar after the system has been mechanically pushed together a distance , by some unknown force F, so that the gap is closed. Clearly draw all required FBDs. Explicitly count, as you write each equation, the number of unknowns and the number of equations. Put each useful equation in a "cloud". Do not solve or simplify the set of equations. Just show that you understand how to set up the equations and what known values would be substituted into each equation. Forbars:E1=E3=210GPaE2=70GPaL=0.3mA1=A3=2A2=0.0004m2