1. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
Body bending strength requirement:
To locate and retain the vehicle subsystem in the correct position
Does not fail under static/dynamic loading conditions
Shear loads & moments can be identified from the S-BM diagrams
All materials in this slide are taken from Donald E Malen Fundamentals of Automobile Body Structure Design, SAE International.

2. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
Severe bending conditions can be occurred due to dynamic loading and
jacking/towing
A factor of 2-g loading is typically used to represent dynamic condition
These two extreme conditions might cause the structure to fail
All materials in this slide are taken from Donald E Malen Fundamentals of Automobile Body Structure Design, SAE International.

3. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
The H Point Bending Test is used to
approximate bending moment envelope
It can be 1 or 2 point loads applied at
the seating location
The H Point Bending Test:
Body is supported at the suspension
attachments
The loads are increased incrementally
and the deflections are recorded until it
reachs permanent deformation
All materials in this slide are taken from Donald E Malen Fundamentals of Automobile Body Structure Design, SAE International.

4. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
Bending stiffness
Can be measured from the load-deflection curve
The reason is to cater for body vibration so that it can achieve the feeling of
solidness
The desired bending frequency is from Hz
Assume that the structure as a uniform beam; the primary bending frequency is
M = wL/g L
Now, with a single static load at its center span, the bending resonant frequency is l
Simply supported
All materials in this slide are taken from Donald E Malen Fundamentals of Automobile Body Structure Design, SAE International.

5. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
Typical values of body strength and stiffness for a mid size vehicle are;
6680 N without permanent deformation
7000 kN/m
All materials in this slide are taken from Donald E Malen Fundamentals of Automobile Body Structure Design, SAE International.

6. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
Load Path Analysis
To meet body strength requirement, the structure must be carefully designed
Only end and shear loads are allowed in the structural surface model
The applied load will represent the bending strength requirement
Each surface must be capable of reacting the loads without excessive
permanent deformation
Example 1
All materials in this slide are taken from Donald E Malen Fundamentals of Automobile Body Structure Design, SAE International.

7. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
All materials in this slide are taken from Donald E Malen Fundamentals of Automobile Body Structure Design, SAE International.

8. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
Analysis of Body Bending Stiffness
Focus on the side frame due to its significant contribution on bending stiffness
The model consists of beams, rigid plates and pin connections
Applied load acts at the center of rocker/end of B-pillar
Approximation of the stiffness is made using finite element method
All materials in this slide are taken from Donald E Malen Fundamentals of Automobile Body Structure Design, SAE International.

9. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
Example of the analysis is given below with the initial guess for beam section size
The result shows that the total bending stiffness is 2088 kN/m
Only 30% of the target value (7000 kN/m)
Change the beams section size/shape. BUT which BEAM?
Example 2
All materials in this slide are taken from Donald E Malen Fundamentals of Automobile Body Structure Design, SAE International.

10. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
Finite element analysis

11. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
Importance of joint flexibility
Previous analysis assumed the beams
were rigidly connected
In reality, when two or more thin-walled
beams are joined, localized deformation
may occur
Thus, it has the effect of a flexible joint
and this can be represented by rotational
spring
The rotational stiffness can be determined
by taking ratio of moment over rotational
angle
All materials in this slide are taken from Donald E Malen Fundamentals of Automobile Body Structure Design, SAE International.

12. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
Joint Efficiency
To check whether the joint stiffness is a very stiff or very flexible
It can be define as the ratio of the combined stiffness of the beam-joint to the stiffness of the beam alone
Example 3
The steel rocker beam has section size of h = 100mm, w = 50mm, t = 1mm
L = 1000mm. Compute the joint efficiency for Hinge pillar to rocker joint.
All materials in this slide are taken from Donald E Malen Fundamentals of Automobile Body Structure Design, SAE International.

13. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
Solution
I = 4.15E+5 mm^4
K = 0.2E+6 Nm/rad from diagram
E = 207 GPa
Joint efficiency, f
= 1/(1 + (2x207000x4.15E5/1000x0.2E6))
= 0.537
The joint reduces ½ of the beam alone
All materials in this slide are taken from Donald E Malen Fundamentals of Automobile Body Structure Design, SAE International.

14. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
Example 4
Consider Example 2 with reasonable joint stiffness to three of the joints.
Re-run FEA.
It is found that the deflection is increased and hence, reduce the bending
stiffness to 1735 kN/m; closer to the test data.
However, the value is far from the target value. HOW to achieve it?
Which beams or joints to adjust?
All materials in this slide are taken from Donald E Malen Fundamentals of Automobile Body Structure Design, SAE International.

15. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
Strain energy and stiffness
As the beams deform under load application, strain energy is stored.
The strain energy can be determined as a function of the end moments
on the beam
- The highest fraction of strain energy will improve stiffness of a structural system
All materials in this slide are taken from Donald E Malen Fundamentals of Automobile Body Structure Design, SAE International.

16. DESIGN FOR BODY BENDING
SMC 4133 AUTOMOTIVE STRUCTURES
DESIGN FOR BODY BENDING
Example 5
Consider the seat mount system consisting of a beam connected by a
Flexible joint to a rocker. The system does not meet the stiffness requirement,.
Which element needs to be changed: the beam or the joint?
Solution
SE beam = 200xM^2/(6x1E10) = 3.33E-9M^2
SE joint = M^2/(2x2E8) = 2.5E-9M^2
The beam stiffness has a larger effect on overall system stiffness
All materials in this slide are taken from Donald E Malen Fundamentals of Automobile Body Structure Design, SAE International.