chapter 6 section 3 4 bending deformation strain and stress in beams l.
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Chapter 6 Section 3,4 Bending Deformation, Strain and Stress in Beams

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Chapter 6 Section 3,4 Bending Deformation, Strain and Stress in Beams. 6.2 Bending Deformation and Strain. Key Points: Bending moment causes beam to deform. X = longitudinal axis Y = axis of symmetry Neutral surface – does not undergo a change in length. Key Points:

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slide2

6.2 Bending Deformation and Strain

  • Key Points:
  • Bending moment causes beam to deform.
  • X = longitudinal axis
  • Y = axis of symmetry
  • Neutral surface – does not undergo a change in length
slide3

Key Points:

  • Internal bending moment causes beam to deform.
  • For this case, top fibers in compression, bottom in tension.
slide4

Key Points:

  • Neutral surface – no change in length.
  • All cross-sections remain plane and perpendicular to longitudinal axis.
  • Neglect deformation of cros section within its own plane.
slide5

Radius of curvature

Length decreases

Length = constant

slide6

Says normal strain is linear

Maximum at outer surface (where y = c)

slide7

6.2 Bending Stress – The Flexure Formula

What about Stress????

Recall from section 6.1:

Therefore, it follows that

slide9

Sum moments about cut:

This is the moment of inertia, I

the flexure formula
The Flexure Formula:

Internal bending moment, lb-in

Max bending stress, psi

Distance from NA to outer fiber, in

Moment of inertia, in4

Or in general:

examples
Examples:
  • Find maximum moment
  • Find area properties, I and c
  • Calculate stress
slide12

WHERE IS BENDING STRESS MAXIMUM???

  • Answer:
  • Outer surface (furthest away from Neutral Axis)
  • Value of x along length where moment is maximum!!
slide16

Example: The T-shape beam is subjected to the loading below.

  • Draw shear and moment diagram. Identify location and magnitude of Mmax.
  • Determine location and magnitude of maximum bending stress and draw stress profile. Is the beam safe if the material is aluminum w/ sy = 15 ksi?
  • What is the largest internal moment the beam can resist if sallow = 2 ksi?
slide18

Statics: Example 1 - Pliers

Given: Typical household pliers as shown.

Find: Force applied to wire and force in pin that connects the two parts of the pliers.

Do this for homework.

See solution Link

Side: what is the shear stress in pin and bending stress in handle? SofM

slide19

Statics: Example 2 – Crane Structure

Given: Crane structure as shown.

Find: Forces and FBD’s for cables A-B and A-E, boom DEF and post AFC.

Do this for homework.

See solution Link

Side: what is the normal stress in cables (average normal only) and normal stress in boom and post (combined loading)? SofM

slide20
Example 4: Determine the resultant internal loadings acting on the cross sections located through points D and E of the frame. (1-114)