The present work deals with the investigation of strength of a specialized chassis mounted platform/structure designed to carry concentrated load. This work deals with the mathematics behind braking through shear and bending diagrams analysis processes. The perceptible loading case in the present analysis comprises braking load and its effect on the platform/structure by usage of simple shear force & bending moment diagrams. These diagrams reveal the distribution of shearing force during braking for typical Indian truck. Present analysis accentuates on the design stage aspects of the platform as this research is a step in doctoral study. Effect of load during braking for an atypical type of combination of longitudinal and cross members in platform/frame design is formulated. This paper provides a new technique for computation of strength using shear and bending diagrams. Peculiarity of this analysis is the usage of combined section modulus of three members for computation of stress.

1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEME
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AN INVESTIGATION OF STRUCTURAL INTEGRITY OF CHASSIS
MOUNTED PLATFORM SUBJECTED TO CONCENTRATED LOAD
DURING BRAKING
Prof.Dr. Matani A.G1
Prof.Deulgaonkar V.R2
Prof.Dr. Kallurkar S.P3
1
(Mechanical Engineering, Govt. College of Engineering, Amravati, Sant Gadge Baba
Amravati university, Amravati, India, ashokgm333@rediffmail.com)
2
(Mechanical Engineering, Govt. College of Engineering, Amravati, Sant Gadge Baba
Amravati university, Amravati, India, vikasdeulgaonkar@gmail.com)
3
(Mechanical Engineering, D.Y Patil College of Engineering, University of Pune, Pune ,
India, drkallurkar@yahoo.co.in )
ABSTRACT
The present work deals with the investigation of strength of a specialized chassis
mounted platform/structure designed to carry concentrated load. This work deals with the
mathematics behind braking through shear and bending diagrams analysis processes. The
perceptible loading case in the present analysis comprises braking load and its effect on
the platform/structure by usage of simple shear force & bending moment diagrams. These
diagrams reveal the distribution of shearing force during braking for typical Indian truck.
Present analysis accentuates on the design stage aspects of the platform as this research is
a step in doctoral study. Effect of load during braking for an atypical type of combination
of longitudinal and cross members in platform/frame design is formulated. This paper
provides a new technique for computation of strength using shear and bending diagrams.
Peculiarity of this analysis is the usage of combined section modulus of three members
for computation of stress.
Keywords: Braking condition, horizontal load, shear stress, Structural strength shear
force and bending moment diagram.
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 4, Issue 1, January- February (2013), pp. 115-122
© IAEME: www.iaeme.com/ijmet.asp
Journal Impact Factor (2012): 3.8071 (Calculated by GISI)
www.jifactor.com
IJMET
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1. INTRODUCTION
The safe and reliable use of a road vehicle necessitates the continual adjustment of its
speed and distance in response to change in traffic conditions. Braking system in every
vehicle plays a vital role in fulfilling this requirement. Design of the braking system which
makes an efficient use as possible of the finite amount of traction available between the tire
and the road over the entire operational range is of prime importance. A detailed torque
characteristics study of small disk brake using magnetic fluid is carried out by Hyung S.B
et.al. The torque characteristic of small disk brake by a magnetic body force is studied
through the relation between magnetic field intensity and rotational disk velocity [2].
Dynamic stability of vehicle is evaluated using real time dynamic stability control system, a
different approach to estimate the vehicle velocity by Li L et.al, [3]. Chul-Goo Kang
analyzed design parameters of the braking system in the development of new high speed
train. He proposed a hardware-in-loop system for the braking system of a Korean high-speed
train [4]. Gyu Ha Kim et.al used a virtual proving ground approach for obtaining the dynamic
stress or strain distribution. Realistic boundary conditions of tire/road surface interactions are
implemented by using the virtual proving ground approach [5].
2. BRAKING MECHANISM MATHEMATICS
Braking performance equation is obtained from Newton’s Second Law applied in
horizontal direction. Applying the Newton’s Law to a light truck loaded with a container, we
get an equation as that relates all the forces exerted during braking. The vehicle weight W is
subjected to a linear deceleration, which is balanced by the total action of front & rear axle
braking force Fxf & Fxr, aerodynamic drag Da, and the sine component of weight all
considered in horizontal direction.
െ
୛
୥
Dx ൌ െFxf െ Fxr െ Da െ Wsinθ ------ (1)
-ve sign is to account for linear deceleration.
For present case linear deceleration is presumed considering the adhesion between tire and
ground. The braking efficiency or the maximum retarding force F, applied by the brakes at
the wheels relies on the friction coefficient between the tire and the road surface and the
component of weight of the vehicle on the wheel. These terms are interrelated as
: F ൌ µW------ (2)
This shows that the braking efficiency is highly affected by the coefficient of friction.
Considering all the on road possibilities, braking efficiency of 50% is hypothesized. The
component of vehicle weight including the laden weight in the container generates a moment
around the centre of gravity of the vehicle. The total weight in present research is so arranged
that it is distributed at six locations on the platform. All these locations are referred to as ISO
corner locations. Total weight of twelve tones is distributed variably at front, middle and rear
ISO coroners. At two front and two rear ISO corners a total load of six tone is applied 1.5
tone at each. A load of six tone is applied at the two mid ISO corners, three tone each on each
side. By considering a braking efficiency of 50%, a horizontal force in addition to vertical

3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
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one acts at each ISO corner. The magnitude of each load is half the load that acts at each ISO
corner. This horizontal force is shear force that induces a shear stress at each ISO corner
location. The magnitude of this stress is estimated using shear force and bending moment
diagrams. The section properties of the individual members i.e. vehicle chassis, main
longitudinal member and square cross member is evaluated in [18]. The combined section
modulus values of the unsymmetrical section are calculated for estimating the stress during
braking condition.
3. ESTIMATION OF SHEAR FORCE, BENDING MOMENT AND STRENGTH OF
THE STRUCTURE
During braking a horizontal load acts on the platform. This load acts in addition to the
load in stationary condition. So, for this case the resultant bending moment is combination of
horizontal and vertical bending moment.
The support reaction calculations are done as below.
ΣFy = RA + RD = 140 KN
ΣMa = Ra x 0 + 35 x 0.7 + 70 x 3.55 – RD x 5.6 + 35 x 7.4
RD = 95 KN (upward)
RA = 140 – RD = 45 KN (upward)
During braking a horizontal force of magnitude equal to half of vertical loads magnitude at
respective ISO corner. This is taken into account by considering a moment around the
centroidal axis of outer longitudinal member.
A sample calculation of shear force and bending moments in transverse direction to outer
longitudinal member is shown in table 1.The calculations for shear force and bending
moment are tabulated below
TABLE 1: Shear force and Bending Moment Sample calculations
Point Shear force calculation (S.F) Bending Moment calculation (B.M)
S.F Just LHS
(KN)
S.F Just RHS
(KN)
B.M Just LHS
(KN-m)
B.M Just RHS
(KN-m)
A 0 45 0 0
B 45 10 31.5 31.5
C 10 -60 60 60
D -60 35 -63 -63
E 35 0 0 0
The shear force and bending moment diagrams for both concentrated load and
concentrated load with moment around each load point is shown in fig1 and fig.2

4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
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Fig.1: Shear Force and Bending Moment Diagram for Concentrated Load

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Fig.2. Shear force and Bending moment diagram for braking condition

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3.1 Stress in the longitudinal member
The resultant bending moment is the vector sum of the maximum bending moments at
the mid ISO corner. So the resultant bending moment is given as
‫ܯ‬ ൌ ඥሺ53.6ሻ2 ൅ ሺ60ሻ2
M = 80.45470776 KN-m.
Using this value of bending moment we further compute stress using the fundamental
bending equation as : ݂ ൌ
ெ
௓
--- (3). Inputting the values of maximum bending moment and
section modulus computed in (3), we get the stress magnitude at braking.
fሺbrakingሻ ൌ
80.45470776
965241.9618
fሺbrakingሻ ൌ 83.351MPa
also as the section being unsymmetrical, the stress induced during braking is evaluated from
both sides.
fሺbrakingሻ ൌ
80.45470776
641454.3918
fሺbrakingሻ ൌ 125.425 MPa
4. CONCLUSION
For the design process of specialized platforms/structures mounted on chassis of truck
or heavy vehicles intended for carrying containers a new method is attempted with the
extension of classical method of stress computation. Estimation of load & stress in
accordance with the static and braking load is done with the aid of classical shear force and
bending moment method for dynamic condition of the vehicle. The stress computed by this
technique is well within permissible limits of yield strength of the material. Furthermore this
method can be extended for estimation of shear stress at the load location during braking.
This method provides a prior approximation of stress and stress distribution in at this variable
loading condition. This method is not accurate as it gives values of stress and strain only at
load location and not at the other locations on the platform. This technique also limits its
application in x and z directions for evaluation of stress and strain values in these directions
cannot be computed.
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