1. STRESS DUE TO BENDING

2. STRESS DUE TO AXIAL FORCES
Stress due to purely axial forces gives direct stress.
–either tensile or compressive.
i.e. The stress is the same value across the section
Distance
Stress F A
stress =
Stress variation across member

3. Consider beam under simple u.d.l.
Distance
Stress
Stress variation across member
Top fibre in compression
Bottom fibre in Tension
Point where tension changes
to compression is called NEUTRAL AXIS
HERE THE STRESS IS ZERO + -

4. Internal Moment of Resistance
Imagine beam cut along section
Imagine forces needed to maintain stability
These two forces constitute a COUPLE which resists the external moment trying to bend the beam.
push
pull

5. = Internal moment of resistance or couple on the beam section
THE EXTERNAL MOMENT AT A SECTION WILL INDICATE THE INTERNAL COUPLE GENERATED INSIDE THE BEAM SCTION F d
Knowing depth of beam will give us the “lever arm” applicable to this couple
Hence we can deduce the tensile and compressive stress on the beam section
External BENDING MOMENT, or applied moment, due to the loading on the beam
= Internal moment of resistance or couple on the beam section
The forces constituting the couple vary along the section due to the variation from compression to tension
The resistance the section offers is dependant on the beam cross sectional shape.
The material of the beam also affects the resistance (or strength)
from the above and with a bit of dfferential calculus we can formulate a general solution to beams in bending.

6. General theory of bending
Where
M = Moment of resistance = Applied external Bending Moment
I = 2nd Moment of Area about the Neutral Axis (also known as Moment of Inertia)
f = permissible stress, or stress in beam material
y = distance from neutral axis to (usually) outer fibre of beam section
E = Young’s Modulus of beam material
R = Radius of curvature of the beam (the deflected shape)

7. I = 2nd Moment of Area
This is an indication of the distribution of, and hence the resistance to bending, of material in the beam cross section.
Also note that the two area properties, I & y can be combined to give the Section Modulus Z .
Units: cm3