FORCE AND SYSTEM

1. AR7202 MECHANICS OF STRUCTURES I L T P/S C
2 2 0 3
OBJECTIVES:
 To make students aware of how structural resolutions are important in realization of
architectural design concept. At this stage, students shall be exposed to forces,
moments, and resolution of forces.
 To make the students understand basic properties of solids and sections which
influence their behavior under the effect of various types of forces.
UNIT I FORCES AND STRUCTURAL SYSTEMS 16
Principles of statics- Forces and their effects-Types of force systems - Resultant of
concurrent and parallel forces--Lami’s theorem- principle of moments -Varignon’s
theorem - principle of equilibrium –Types of supports and loadings –Determination of
reactions for simply supported beams - simple problems.
UNIT II ANANLYSIS OF PLANE TRUSSES 12
Analysis of plane trusses - Introduction to Determinate and Indeterminate plane
trusses - Analysis of simply supported and cantilevered trusses by method of joints
and method of sections.
UNIT III PROPERTIES OF SECTION 12
Properties of section -Centroid- Moment of Inertia - Section modulus – Radius of
gyration - Theorem of perpendicular axis - Theorem of parallel axis –simple
problems.
UNIT IV ELASTIC PROPERTIES OF SOLIDS 10
Elastic properties of solids –concept of stress and strain –deformation of axially
loaded simple bars-types of stresses- Concept of axial and volumetric stresses and
strains. (excluding composite bar).
UNIT V ELASTIC CONSTANTS 10
Elastic constants –Elastic Modulus-Shear Modulus- Bulk Modulus-Poisson’s ratio -
Relation between elastic constants - Application to problems.
TOTAL: 60 PERIODS
OUTCOMES:
 Apply the concepts of action of forces on a body and should be able to apply the
equilibrium concepts.
 Students are taught basic geometric properties and the behavior of materials under
effect of forces.

2. FORCES AND STRUCTURAL SYSTEMS
UNIT 1

3. SYLLABUS
• Principles of statics- Forces and their
effects-Types of force systems - Resultant
of concurrent and parallel forces--Lami’s
theorem- principle of moments -Varignon’s
theorem - principle of equilibrium –Types
of supports and loadings –Determination
of reactions for simply supported beams -
simple problems.

4. PRINCIPLES OF STATICS
• Statics is a branch of mechanics which studies
the effects and distribution of forces of rigid
bodies which are and remain at rest.
• In this area of mechanics, the body in which
forces are acting is assumed to be rigid. The
deformation of non-rigid bodies is treated in
Strength of Materials.

5. • Principles of statics consists of the study of
structures that are at rest under static
equilibrium conditions. To ensure equilibrium,
the forces acting on a structure must balance,
net torque acting on the structure should be
zero.
• The static analysis methods provide the means
to analyze and determine both internal and
external forces acting on a structure.
• For structures in a plane, three equations of
equilibrium are used for the determination of
external and internal forces.

6. • A statically determinate structure is one in which all the
unknown member forces and external reactions may be
determined by applying the equations of equilibrium.
• An indeterminate or redundant structure is one that
possesses more unknown member forces or reactions
than the available equations of equilibrium.
• These additional forces or reactions are termed
redundants. To determine the redundants, additional
equations must be obtained from conditions of
geometrical compatibility.
• The redundants may be removed from the structure, and
a stable, determinate structure remains, which is known
as the cut-back structure.
• External redundants are redundants that exist among the
external reactions. Internal redundants are redundants
that exist among the member forces.

7. conditions of equilibrium of forces

8. CONDITIONS OF EQUILIBRIUM
• In order to apply the principles of statics to a structural system,
the structure must be at rest. This is achieved when the sum of the
applied loads and support reactions is zero and there is no
resultant couple at any point in the structure. For this situation,
all component parts of the structural system are also in
equilibrium.
• A structure is in equilibrium with a system of applied loads when
the resultant force in any direction and the resultant moment
about any point are zero. For a system of coplanar forces this
may be expressed by the three equations of static equilibrium:
• ΣH = 0
ΣV = 0
ΣM = 0
• where H and V are the resolved components in the horizontal and
vertical directions of a force and M is the moment of a force about
any point.

9. STATIC EQUILIBRIUM
Forces acting in one plane (i.e., coplanar) and in
equilibrium must satisfy one of the following sets of
conditions:
Fx=0 Fx=0 Fy=0 Ma=0
Fy=0 or Ma=0 or Ma=0 or Mb=0
Ma=0 Mb=0 Mb=0 Mc=0
where F refers to forces and M refers to moments of
forces.

10. When forces acting on an object which is at rest are balanced, then we say that the object is in
a state of static equilibrium.
The resultant of these forces equals zero. That is, the vector sum of the forces adds to zero.
Example #1
Suppose two dogs are struggling for the same shoe as shown in the diagram below.
The left dog's force is shown by the yellow/black arrow while the right dog's force is shown by
the teal arrow. Notice below that when the forces are added head-to-tail, the resultant force,
shown in grey, acts straight up the y-axis.

11. Force
A force is any cause which tends to alter the state or rest
of a body or its state of uniform motion in a straight line.
A force can be a quantitatively as the product of the
mass of the body, which the force is acting on, and the
acceleration of the force.
F = ma , where
F = applied force
m= mass of the body ( kg)
a = acceleration caused by the force (m/s2)
The Sl units for force are therefore kg m/s2 which is
designated a Newton (N). The following multiples are
often used:
1kN = 1,000N, 1MN = 1,000,000N

14. The Effects of Forces
• A force acting on an object may cause the
object to change shape, to start moving, to stop
moving, to accelerate or decelerate.
• When two objects interact with each other they
exert a force on each other, the forces are
equal in size but opposite in direction.

15. TYPES OF FORCE SYSTEMS
CONCURRENT FORCES

16. NON CONCURRENT FORCES

17. COPLANER FORCES

18. NON COPLANER FORCES

19. PARALLEL FORCES

20. COLLINEAR FORCES

21. COLLINEAR FORCES

22. Resultant force
The forces acting on an object can be replaced
with a single force that causes the object to
behave in the same way as all the separate forces
acting together did, this one overall force is
called the resultant force.
All forces (F) are measured in newtons (N).

26. If the resultant force acting on an object is
ZERO then;
• the object will remain stationary if it was
stationary when the resultant force became
zero
• move at a constant (steady) speed in a straight
line if it was moving when the resultant force
became zero

27. EQUILIBRANT FORCE (E)