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INTERNAL FORCES IN BARS

INTERNAL FORCES IN BARS. L. Bar axis. H. B. Definitions. Bar – a body for which L»H,B Bar axis - locus of gravitational centres of bar sections cutting its surface Prismatic bar – when generator of bar surface is parallel to the bar axis Straight bar – when bar axis is a straight line.

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INTERNAL FORCES IN BARS

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  1. INTERNAL FORCESIN BARS

  2. L Bar axis H B Definitions • Bar – a body for which L»H,B • Bar axis - locus of gravitational centres of bar sections cutting its surface • Prismatic bar – when generator of bar surface is parallel to the bar axis • Straight bar – when bar axis is a straight line

  3. P M q . M Assumptions • Bar axis represents the whole body and loading is applied not to the bar surface but the bar axis • Set of bar and loading will be considered as the plane one if forces acts in plane of the bar.

  4. n n O z x y Agreements • Reduction centreO is located on the bar axisby vectorr0 • Internal forces are determined on the planes perpendicular to the bar axis (vector n is parallel to the axis) • Vector nisan outward normal vector r0

  5. Swz Mwz Sw Mw z Swx Mwx Sny Mwy x y In 3D vectors of internal forces resultants have three components each Sw{ Swx , Swy , Swz} Mw{Mwx , Mwy , Mwz} Components of internal forces resultantsSwx , Swy , SwzandMwx , Mwy , Mwzare calledcross-sectional forces

  6. n n n n n . . . . . Sw= Sw(rO , n) Mw= Mw(rO , n) Resultants of internal forces are vector functions of two vectorsroandn Vector nis known if we know the shape of bar axis Thus, resultants of internal forces for known bar structure are function of only one vector r0 Sw= Sw(rO) Mw= Mw(rO)

  7. P Sz z x q Sx y My . M M In 2D number of cross-sectional forces is reduced, because loading and bars axes are in the same plane (x, z): Sw{ Sx , 0, Sz} Mw{ 0, My , 0 } We will use following notations and names for these components: Sx=N - axial forces Sz=Q - shear force My = M - bending moment

  8. Special cases of internal forces reductions are called: N TENSION – when internal forces reduce to the sum vector only, which is parallel to the bar axis SHEAR – when internal forces reduce to the sum vector only, which is perpendicular to the bar axis Q M BENDING – when internal forces reduce to the moment vector only, which is perpendicular to the bar axis TORSION – when internal forces reduce to the moment vector only, which is parallel to the bar axis Ms

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