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 - PowerPoint PPT Presentation

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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### Chapter 6Section 3,4Bending 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:

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

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.

Length decreases

Length = constant

Says normal strain is linear

Maximum at outer surface (where y = c)

6.2 Bending Stress – The Flexure Formula

Recall from section 6.1:

Therefore, it follows that

This is the moment of inertia, I

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

WHERE IS BENDING STRESS MAXIMUM???

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

• 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?

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.

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

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.