1153 Words5 Pages

Bending Stress and its Distribution Induced in a Section
Learning Objectives:
To calculate the value of bending stress at a given point in a section To understand the nature of bending stress To understand the distribution of bending stress cross a section To appreciate the way to reduce the bending stress without using more material
My I cz
Worked Example: Calculate the Maximum Stresses in the Beam y P=10kN A
2m
K
B
2m
K
C
250
c
z
60
RAy
Rcy
Section K-K through Beam
Assuming that the beam has a uniform section
Determine
the section where maximum bending moment occurs Work out the stress distribution at the section due to the maximum BM
Slide 6
Slide 5
Determine the Location(section) Where the Maximum Bending Moment Occurs
Sketch SF and BM diagrams
O
P=10kN A
2m
B
2m
C
x
Rcy=5kN 5 -5
Locate the section Ray=5kN along the total span of the beam where SF 5 BM takes its O maximum value
Gain the value of the maximum banding moment BM
x
-5 x
10kNm
O At section B, BM takes maximum value: M=BM=10kNm
Determine both Centroid and Second Moment of Area for Section B
K
y
P=10kN A
2m
B
2m
K
C
250
c
z
y 125
60
Ray=5
cz
Rcy=5
will be neutral axis WHY? “d” is the side of 250mm Centroid can be given y d / 2 250 / 2 125mm Icz = Igz and can be calculated
Section K-K through Beam
bd 3 60 2503 =78,125,000 mm4 I cz 12 12
Stress Distribution Cross Section Under the Bending Moment (M=BM=10kNm) y S
3
My I cz
c
y
z
Direct stress at position S within the section is resulted from the bending moment M in the section y is the PERPENDICULAR distance of any position S to the neutral axis within the section
Icz is the second moment of area for the section
is proportional to the distance y
Slide 3
Slide 3
Bending Stresses at Three Typical Points within the Section
Stresses at point

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