week6-1 - Bending Bending Transverseloadscausethebeamtobend

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
ending Bending Transverse loads cause the beam to bend rather than stretch, compress or twist. The deformed shape is called the deflection curve or elastic curve.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ending Bending x y plane is the plane of bending. Bending (or flexure) is said to occur about the z axis
Background image of page 2
ending Bending Longitudinal symmetry means the member cross section, support conditions and applied loads are symmetric to the longitudinal plane.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ending Bending If we consider the beam to be made up of imaginary fibers that run parallel to the longitudinal axis, then e can see the bers at the top are in compression we can see the fibers at the top are in compression , and the fibers at the bottom are in tension .
Background image of page 4
ure Bending Pure Bending Regions subjected to a constant bending moment (and no axial forces) are in ure bending pure bending. These are regions where ear force equals zero. shear force equals zero.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
on niform Bending Non uniform Bending For non uniform bending ending moment changes (bending moment changes along the span of the beam), our analysis will apply if the length is great compared to the cross sectional dimensions.
Background image of page 6
exural Strains Flexural Strains Assumptions Beam was straight before bending occurs Beam cross section is nstant constant. Sections h h and k k were lane surfaces before plane surfaces before deformation and remain plane surfaces after.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
exural Strains Flexural Strains After bending Fibers on the top surface of beam get shorter Fibers on the bottom surface of the beam get longer. A surface, the neutral surface , within the beam does not change length
Background image of page 8
exural Strains Flexural Strains After bending The beam deformation takes the shape of a circular arc with a center of curvature O . The radial distance from the neutral surface to the center of curvature is the dius of curvature ( radius of curvature ( ρ ).
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ormal Strain of a Longitudinal Fiber Normal Strain of a Longitudinal Fiber riginal length Original length New Length x x Δ Δ Strain x x x L e x x Δ Δ Δ = = Δ 0 lim ε θ ρΔ = Δ x Expressed as arc lengths () ρ Δ = Δ y x
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/01/2009 for the course CIVE 207 taught by Professor Shao during the Winter '09 term at McGill.

Page1 / 41

week6-1 - Bending Bending Transverseloadscausethebeamtobend

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online