Post on 18-Dec-2015
Key Points:
1. Bending moment causes beam to deform.
2. X = longitudinal axis
3. Y = axis of symmetry
4. Neutral surface – does not undergo a change in length
6.2 Bending Deformation and Strain
Key Points:
1. Internal bending moment causes beam to deform.
2. For this case, top fibers in compression, bottom in tension.
Key Points:
1. Neutral surface – no change in length.
2. All cross-sections remain plane and perpendicular to longitudinal axis.
3. Neglect deformation of cros section within its own plane.
max
c
y
6.2 Bending Stress – The Flexure Formula
What about Stress????
Recall from section 6.1:
Therefore, it follows that
max
c
y
The Flexure Formula:
I
Mcmax
I
MyOr in general:
Max bending stress, psi
Internal bending moment, lb-in
Distance from NA to outer fiber, in
Moment of inertia, in4
WHERE IS BENDING STRESS MAXIMUM???
Answer: • Outer surface
(furthest away from Neutral Axis)
• Value of x along length where moment is maximum!!
Example: The T-shape beam is subjected to the loading below.
1. Draw shear and moment diagram. Identify location and magnitude of Mmax.
2. 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?
3. 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.
Side: what is the shear stress in pin and bending stress in handle? SofM
Do this for homework.
See solution Link
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.
Side: what is the normal stress in cables (average normal only) and normal stress in boom and post (combined loading)? SofM
Do this for homework.
See solution Link