This document discusses bending moment stress, including uniaxial and biaxial bending stress. It defines bending as causing deflection from a straight line, and bending moment as a measure of bending force applied at a distance from a beam's neutral axis. Bending moment stress induces tension or compression in a bent body. Examples show calculations for uniaxial 3-point and 4-point bending stresses, as well as an example of biaxial bending stress distribution and the line of zero stress in a loaded block.

1. BENDING MOMENT
STRESS
(UNI AXIAL & BI AXIAL)
SERAJUS SALEKIN TANVIR
STUDENT ID: 10.01.03.089

2. What is Bending?

Bending is the present participle of the word
bend which means to cause something to
deflect from the straight line or to make
something have a curved shape.

3. What is Bending Moment?

A bending moment is a measure of the
bending effect due to forces acting on a beam.
It is a type of stress and is measured in terms
of force and distance.

4. What is Bending Moment Stress?
 Bending moment stress is the normal
stress that is induced at a point in a body
subjected to loads that cause it to bend.
 An internal tensile or compressive stress
developed in a beam in response to
curvature induced by an external load.

5. In Diagram, a simply supported beam loaded at
the center. It deflects under the load . When
examining bending moments, horizontal forces
act on the cross sectional face of the beam
section.

6. In Diagram 2, here is the left end section of the beam. It
shows the horizontal forces along the top and bottom in
Diagram 2a, but the forces act across the whole cross
section as shown in the side view in Diagram 2b. The
horizontal forces decrease from maximum at the outer
edges to zero at the neutral axis (an axis running through
the centroid of beam cross section).

7. The maximum "Bending Stress" at some location
along the beam is equal to the bending moment,
M, at that location "times" the distance, y, from
the neutral axis to the outer edge of the beam
"divided" by the moment of inertia, I, of the beam
cross sectional area.
σ =M y / I

8. Why Bending Moment Stress is
necessary for design?
To verify the design for safety of the
structure and the users.
 To understand the results obtained from
design analysis, it is necessary to have the
theoretical knowledge of the bending
moment stresses developed in various
loading conditions.


9. What is Uniaxial Bending Stress?
 uni
axial bending stress is the stress
that is generated when a structure
is bend about one axis.
 The 3-point or 4- point bending
setups represent this type of
bending.

10. In 3 point and 4 point bending setups ,the
sample is placed on parallel support roller
and bended by another set of rollers.
 During bending the top surface is in
compressive stress state and the bottom
surface is in a tensile stress state.


11. The bending stress can be calculated for
small deflection,
For 3 point bending, σ= 3FI/2bd^2
For 4 point bending, σ= 3F/2bd^2(L-L1)
Where,
load span for L ,
the width b ,thickness d
and applied force F.

12. Practical Example of 3 point loading

13. Practical Example of 4 point loading

14. What is Biaxial Bending Stress?
In Biaxial bending test, stress state is
biaxial. In comparison to uniaxial bending
stress, biaxial bending often occurs in
application.
 There are various setups of biaxial bending
test. Among them ring-on-ring test and
ball-on-ring test commonly used.
 Some other test methods are piston-on-3
balls test ,ball-on-3-ball test, 3-ball-on-3balls test ,ball breaker test etc.


15. 
EXAMPLE OF BIAXIAL BENDING STRESS
PROBLEM:
1)Find the stress distribution at the section ABCD for the
block shown in figure if P=64 KN
2)At the same section find the line of zero stress

16. EXAMPLE OF BIAXIAL BENDING STRESS
SOLUTION:
 Moment of inertia about Y-axis and Z-axis,
Iy= 150*300^3/12=337.5*10^6 mm^4
Iz= 300*150^3/12=84.38*10^6 mm^4
 Area of the section ABCD,
A=150*300=45000 mm^2
 Moment about Y-axis and Z-axis,
My=Pz=64*10^3*150=9.6*10^6 N-mm
Mz=Py=64*10^3*(75+75)=9.6*10^6 N-mm


17. EXAMPLE OF BIAXIAL BENDING STRESS
Now we can calculate,
P/A=64*10^3/45000
=1.42 MPa
MyZ/Iy=(9.6*10^6 *150)/337.5*10^6
=4.27 MPa
MzY/Iz=(9.6*10^6 *75)/84.38*10^6
=8.53 MPa

18. EXAMPLE OF BIAXIAL BENDING STRESS
Now stress at a point can be determined,
σ= -P/A± MyZ/Iy ±MzY/Iz
Stress at point A,B,C,D can be calculated
σ at A = -1.42-4.27-8.53=-14.22 MPa
σ at B = -1.42+4.27-8.53=-5.68 MPa
σ at C = -1.42+4.27+8.53=+11.38 MPa
σ at D = -1.42-4.27+8.53=+2.84 MPa

19. EXAMPLE OF BIAXIAL BENDING STRESS
Here in this example, we can see that due to the application of
load, here occurs biaxial bending situation. In this problem we
observed that on A side here occurs maximum compressive
stress=-14.22MPa and on C side here occurs maximum tensile
stress=+11.38MPa.

20. Practical example of Biaxial bending

21. THANK YOU
For your attention…