TorsionBending Deformation of a Straight Member
The Flexure Formula
Arc length = Radius x
If the radius is reduced then so too is the arc length resulting in compression
is known as the radius of curvature and is the distance from the centre of the bend radius to the neutral axis
13MMA100 Mechanics of Materials
This can be expressed as
i.e. Ext/Orig. Length
+y => contraction (-ve strain)
-y => expansion (+ve strain)
Which leads to
i.e. The stress increases linearly with distance from the neutral axis
13MMA100 Mechanics of Materials
Because the resultant force over the cross-section must be zero
Therefore
which can only be satisfied if the horizontal centroidal axis is also the neutral axis
13MMA100 Mechanics of Materials
Flexure Formula
The moment due to the stress distribution should be equivalent to the internal moment
So that
13MMA100 Mechanics of Materials
acts
13MMA100 Mechanics of Materials
The flexure formula is:
What are the max. normal stresses at D and A?
N
A
First consider the load. Total load = ...........
Equates to a single load at position..........
R1 =
R2 =
Draw the left hand beam section using the correct shear and moment convention for the section a-a
Calculate the bending moment
13MMA100 Mechanics of Materials
The flexure formula is .....
What theory do we need to use to find I?
I flange (the vertical bit) =
I web (top and bottom bits!) =
Area of web =
I web (relative to flange centroid) =
Total I value for beam =
13MMA100 Mechanics of Materials
Stress at A =
Stress at D =
Strain varies linearly with distance from NA
Internal moments can be calculated using Flexure Formula
13MMA100 Mechanics of Materials
b
h
What are the max. Normal stresses at D and A?
N
A
Internal Moment
By symmetry, the reaction forces must be R1 = R2 = 15 kN
M
V
Therefore
N
A
s is the normal stress at y
13MMA100 Mechanics of Materials
Coursework due Monday 11th November 2013 before 9 a.m.
s
s
s
s
D
D