This document provides an overview of structural analysis presented by Hassan Abba Musa. It defines structural analysis as predicting the response of a structure to various loads. Loads are classified as dead loads from the structure's weight and imposed loads like wind and seismic forces. Structural analysis ensures equilibrium, displacement compatibility, and force-displacement relationships. Different structural elements, analysis techniques, and matrix operations are also introduced.

1. REVIEW OF
BASIC
STRUCTURAL
ANALYSIS
PRESENTED BY:
HASSAN ABBA MUSA
1401306006

2. #1 - INTRODUCTION TO STRUCTURAL
ANALYSIS
Structural Analysis is the analysis of a given structure
subject to some given loads, and the idea is to predict the
response of the structure (system), thus there are some
inputs referred to as ‘’stimulus’’ and an outputs referred to
as ‘’response’’. The Structural analysis is the application
of solid mechanics to predict the response (Interms of
forces & displacements) of a given structure (existing or
proposed) that subjected to a specified loads.
LOADS
(INPUTS)
RESPONSE
(INPUTS)
STRUCTURE (SYSTEM)

3. Loads are classified into 2 parts:
 Dead loads (Self-weight; of the components of the
structure).
 Imposed loads & forces (Live, Wind, Snow, Rain, and
Temperature, Erection loads, Seismic forces & others).
The Structural Analysis is only ascertained correct
when the following requirements were satisfied;-
 Equilibrium Forces.
 Compatibility of Displacement.
 Force/Displacement Relations.
Therefore, In every forms of the structures, the
structural Engineer has to consider the following
structural considerations and purposes.

4.  Stability,
 Strengths,
 Stiffness,
 Economy, as well as
 Aesthetic aspects of the structure.
The following Softwares are available
 Orion,
 STAAD III,
 ANSYS,
 AXIS VM,
 ETABS, SAP, Etc

5. #2 – DIFFERENT TYPES OF SUPPORTS
 Roller,
 Pinned,
 Hinged,
 Fixed,
 Link,
 Ball and Socket,
 Rigid Support,
 Spring Support.
FORCES

6. #2 – DIFFERENT TYPES OF STRUCTURES
 Frame Structure,
 Truss Structure,
 Shell Structure,
 Arch Structure,
 Suspension Structure,
 Mass Structure, &
 Composite Structure.

8. #3 – LIST OF EQUILIBRIUM EQUATIONS
For state of static equilibrium to exist, it is necessary that the
combined resultant effect of the system of forces shall be neither
a Force nor a Couple; otherwise there will be tendency for
motion of a body. However, many 3D structures are idealized as
series of 2D components:
 If the combined resultant effect of a general system of forces
acting on a planar structures is not be equivalent to a resultant
force, the algebraic sum of all F푥 components must be equal to
Zero and the algebraic sum of all F푦 components must to be
equal to Zero, i.e F푥 = 0 F푦 = 0.
 If the combined resultant effect is not to be equivalent to a
couple, the algebraic sum of the moment M푧 of all forces
about any axis parallel to the Z-reference axis and normal to
the plane of the structure must be equal to zero, i.e M푧 = 0 .

9. #4 – DETERMINATE AND INDETERMINATE
OF A STRUCTURE
If the number of unknown forces is identical to the
number of equilibrium equations, the problem is said to
be Statically Determinate since the unknown forces can
be determined directly from the equilibrium.
2푗 = 푚 + 푟 푤ℎ푒푟푒 푛 = 0
If, however the number of unknown forces exceeds the
number of equilibrium equations, the problem is said to
be Statically Indeterminate to a degree equal to this
excess.
2푗 > 푚 + 푟 푤ℎ푒푟푒 푛 ≠ 0
푗 = 푁표. 표푓 푗표푖푛푡푠, 푚 = 푁표. 표푓 푚푒푚푏푒푟푠,
푟 = 푁표. 표푓 푟푒푎푐푡푖표푛푠

11. #5 – TECHNIQUES USED IN ANALYSING
STRUCTURE
 Macaulay’s Method
 Moment Area Method
 Conjugate Beam Method
 Virtual Work Method
 Unit load Method
 Influence line theory
 The Three Moment Equation (Clapeyron’s Theorem)
 Stiffness & Flexibility Method
 Slope Deflection Method
 Moment Distribution Method

12. MACAULAY’S METHOD
This is a method suggested by W. H. Macaulay to relate
the stiffness, radius of curvature, deflection and the
bending moments in a beam by integration methods.
Beam Deflections using successive integration;
Consider an infinitely small
Section, dx, of the above loaded
beam;

13. MOMENT AREA METHOD
 This is a method suitable for calculating slope &
deflection at selected points on a beam.
 It is also effective for calculating the deflections of
beams with various cross sections.
 The simplest way to evaluate the fixed -end moments,
etc, will often be by the use of the Moment area method.
There are two theorems associated with the moment area
methods:
First Moment Area Theorem:
“The difference in slope between two points on a beam is
equal to the area of the M/EI diagram between the two
points.”

14. Second Moment Area Theorem:
“The moment about a point A of the M/EI diagram between
points A and B will give the deflection of point A relative
to the tangent at point B.”
First Moment Area Theorem
Second Moment Area
Theorem

15. #6 – INTRODUCTION TO
FLEXIBILITY/STIFFNESS METHOD
Flexibility Method (Force Method of Analysis)
In this method, the degree of statical indeterminacy is
initially determined. Thereafter, a number of releases equal to
the degree of statical indeterminacy is introduced, each
release being made by the removal of an external or internal
force. Hence, the forces on the original indeterminate
structure are calculated as the sum of the correction forces
(redundants) and forces on the released structure. Flexibility
Matrix [ f] ;- [f]{F} = {Δ − 퐷}
D represents inconsistencies in deformation while {F}
represents the redundants, Δ Elements represent prescribed
displacements at their respective coordinates. The column
vector {Δ - D} thus depends on the external loading.

16. Stiffness Method (Displacement Method of Analysis)
The displacement method can be applied to statically determinate
or indeterminate structures, but is more useful in the latter,
particularly when the degree of statical indeterminacy is high.
In this method, one must first determine the degree of kinematic
indeterminacy. A coordinate system is then established to identify
the location and direction of joint displacements. Restraining
forces equal in number to the degree of kinematic indeterminacy
are introduced at the co-ordinates to prevent the displacement of
the joints. Stiffness Matrix [S];-
{D} = [푆]−1{-F}
The elements of the vector {D} are the unknown displacements.
The elements of the matrix [S] are forces corresponding to unit
values of displacements.
The column vector {F} depends on the loading on the structure.

17. #3 – MATRIX OPERATIONS
Let A, B, and C be mxn matrices. We have
Properties involving Addition.
1. A+B = B+A
2. (A+B)+C = A + (B+C)
3. A+0 = A where is the mx zero-matrix (all its entries
are equal to 0);
4. A+B = 0, if and only if B = -A.