1 / 15

Strength of materials

Statically Determinate and Indeterminate System of Bars. Strength of materials. 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

shania
Download Presentation

Strength of materials

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Statically Determinate and Indeterminate System of Bars Strength of materials

  2. 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

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

  4. Statically Determinate System of Bars B All bars have the axial rigidity EA 2 S2   1 C C S1 A F F l

  5. Statically Determinate System of Bars Calculating S1 and S2 in the bars, as follow : Calculating elongation li of the bars

  6. Statically Determinate System of Bars

  7. Statically Determinate System of Bars

  8. STATICALLY DETERMINATE SYSTEM OF BARS Any questions ?

  9. 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.

  10. Statically Indeterminate System of Bars An example …

  11. Statically Indeterminate System of Bars From figure (b) , we can get : (a) The elongations of the bars are given by : (b)

  12. Statically Indeterminate System of Bars (c) With (a) and (b), and l1= l / cos, we can get : The vertical displacement :

  13. STATICALLY INDETERMINATE SYSTEM OF BARS Any questions?

  14. Statically Determinate System of Bars Try to solve it … 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.

  15. 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.

More Related