Statically Determinate and Indeterminate System of Bars

Statically Determinate System of Bars  Investigation to trusses and to structures which consist of bars and rigid body  Assumption : the elongations are small as compared with the length of the bars  Applying the equilibrium conditions to the undeformed system

Statically Determinate System of Bars B A C  1 2 F l All bars have the axial rigidity EA

Statically Determinate System of Bars B A C  1 2 F C  S2S2 F S1S1 l All bars have the axial rigidity EA

Statically Determinate System of Bars Calculating S1 and S2 in the bars, as follow : Calculating elongation  l i of the bars

Statically Determinate System of Bars

STATICALLY DETERMINATE SYSTEM OF BARS

Statically Indeterminate System of Bars  A system of bars is statically indeterminate of degree n if the number of unknowns exceeds the number of the equilibrium conditions by n.  In order to determine the forces in the bars of such a system, n compatibility conditions are needed in addition to the equilibrium conditions.  Solving this system of equations yields the unknown forces in the bars.

Statically Indeterminate System of Bars

From figure (b), we can get : The elongations of the bars are given by : (a) (b)

Statically Indeterminate System of Bars (c) With (a) and (b), and l 1 = l / cos , we can get : The vertical displacement :

STATICALLY INDETERMINATE SYSTEM OF BARS

Statically Determinate System of Bars The truss is subjected to a force F. Given: E = 2· 102 GPa, F = 20kN. Determine the cross-sectional area of the three members so that the stresses do not exceed the allowable stress σallow = 150 MPa and the displacement of support B is smaller than 0.5 ‰ of the length of bar 3.

Statically Indeterminate System of Bars To assemble the truss in Fig. (a), the free end of bar 3 (length l − δ, δ<<l) has to be connected with pin C. a) Determine the necessary force F acting at pin C (Fig. b). b) Calculate the forces in the bars after the truss has been assembled and force F has been removed.