1. THEORY & DESIGN OF
STRUCTURES
C3 -05 (5S3 NVQ 2045)
Eng. Y.A.P.M Yahampath
B Sc. Eng (Hons), Dip Highway & Traffic Eng, AMIESL, AMECSL
2. Lecture Hours Allocated
Lecture / Tutorial Practical Demonstrations/
Industrial visits
Self Study Total
72 Hrs 00 Hrs 38 Hrs 110 Hrs
Unit Title Time (Hrs)
Combined Direct & Bending stresses 10
Principle stresses & strain 06
Structural design principles 06
Designing of Reinforced concrete
elements
26
Design of structural steel elements 18
Structural detailing 06
Total 72
3. AIM OF THE MODULE
To develop fundamental understanding of the behavior of structures with
particular reference to statically determinate civil engineering structures.
To develop & understanding of the factors and constraints in determining
suitable structural components.
To develop awareness of the economical, Engineering & esthetic aspect
in designing in selecting a particular structural component for given
condition.
To introduce students to use codes of practice and design charts/ Tables
etc. for designing of structural elements.
4. State Of Equilibrium
• The equilibrium condition of an object exists when Newton's first law
is valid.
• An object is in equilibrium in a reference coordinate system when all
external forces (including moments) acting on it are balanced.
• This means that the net result of all the external forces and moments
acting on this object is zero.
5. Statics
• Statics is the study of bodies and structures that are in equilibrium.
• For a body to be in equilibrium, there must be no net force acting on
it. In addition, there must be no net torque acting on it.
6. The Equation Of Equilibrium
The equation of equilibrium are, Sum of the moment about any point is
zero.
The equation of equilibrium are,
• Sum of horizontal force is zero,
• Sum of vertical force is zero,
• Sum of the moment about any point is zero.
9. Statically Determinate And Indeterminate Structures
• There are two types of structure to be design and analysis in civil
engineering.
• they are Statically determinate and indeterminate structures.
10. Statically Determinate Structure
A statically determinate structure is one where there is only one distribution of internal forces
and reactions which satisfies equilibrium.
If the structure can be analyzed by use of the equation of equilibrium is known as statically
determinate structure.
In a statically determinate structure, internal forces and reactions can be determined by
considering nothing more than equations of equilibrium.
The equation of equilibrium are, Sum of the moment about any point is zero.
The equation of equilibrium are,
Sum of horizontal force is zero,
Sum of vertical force is zero,
Sum of the moment about any point is zero.
.
11. Example of statically determinant structure
At (A) it is hinged support and at (B) it has roller support.
So, In the above beam, the reaction occurred at A is vertically upward
and also in a horizontal direction. Because hinge support has two
reactions.
But, the reaction occurred at B is only one reaction which is vertically
upward.
So, in the above beam, Totally three unknown reaction which is two
reactions at support (A) and one unknown reaction at (B).
So, this beam can be analyzed with the help of those three equilibrium
reaction.
If the number of unknown reactions is less than or equal to equilibrium
reaction i.e three then the structure can be easily analyzed. and this
structure is known as a statically determinant structure.
12. Statically Indeterminate Structure
The structure which cannot be analyzed by just using the equation of equilibrium is
known as a statically indeterminate structure.
13. Example Of Statically Indeterminate Structure
• The above beam, It has two hinge
support in which, (A) has two reactions
and (B) has also two reactions.
• So, the total unknown reaction is four
which is greater than the equilibrium
equation which is only three.
• So, we can not analyze this structure.
So, these types of structures are known
as statically indeterminate structures.
14. Load Path On Structure
• If you see in the residential building
then all the members like a beam,
column, slabs are fixed with each
other. So, they have a more
unknown reaction than the
equilibrium equation which is three.
• Hence, they are statically
indeterminate structure.
17. TYPES OF LOADS ACTING ON STRUCTURE
Loads acting on building
Vertical loads
Dead loads
Live loads
Impact loads
Horizontal loads
Wind loads
Earthquakes loads
Longitudinal Loads
18. Dead loads
• Dead load consists of the weight of the structural members that make up the
structure.
• This could include the buildings insulation, drywall, wood studs, flooring, brick
veneer etc.
• Individually these items may seem fairly light, but when their weights are all
added together it can account for a significant amount of weight applied to the
structure.
• These loads are in addition to the self weight of the structure which could include
the weight of the floor/roof decking and joists, beams, bearing walls, columns,
bracing etc.
• Dead loads are always present throughout the lifetime of a structure, compared
to live loads which can come and go.
19. Live loads
• Live loads are loads imposed on a structure that are made up by the
people who use the structure and what they decide to place in the
structure (furniture/storage etc.).
20. Snow and rain loads
• The weight of snow and rain should not be ignored as it its weight
after an extreme storm can often be heavier than the weight of the
roof structure that supports it
21. Horizontal/lateral loads
• The lateral loads that are applied to structures include wind, seismic
and earth loads. These loads act in the direction perpendicular to the
buildings wall and roof systems.
• Lateral loads on a building are usually resisted by walls and bracing.
• When you see large steel X’s in the windows or exposed elsewhere in
a building, this is often one of the elements used to resist lateral loads
imposed on the structure.
22. Wind Loads
• Wind loads can be applied towards a surface of a building/structure
but it can also be applied away from the building causing a suction
force. These are called positive and negative pressures.
• Wind loads on a structure get greater the higher they are applied to a
structure. On a high rise building, the wind pressures are significantly
higher at the peak of the structure compared to at the ground level.
• If you have ever been outside during an intense windstorm you can
understand how large these wind forces can be and why it is so
important to design a structure to resist these loads.
23. Earthquakes
• Earthquakes are what cause seismic loading on a structure.
• Seismic loads used in designing structures vary depending on where
the structure is relative to seismic zones and the potential for
earthquakes
24. Earth loads
• Earth loads occur when soil is built up against a wall causing lateral earth pressures.
• These loads can be seen on basement foundation walls, retaining walls and tunnels.
• The magnitude of this lateral load is dependent on the type of soil built up against the
structure and the depth of the soil.
• A house with a very high basement would likely have foundations walls that would
have to resist high lateral loading from the soil built up against it if the basement was
fully underground. This can be one of the causes of cracking seen in basement walls if
the wall was not built strong enough to resist these lateral loads.
• If water is allowed to build up against a wall, lateral loads from hydrostatic pressure
would need to be designed for. Installing a weeping tile system is a way to prevent
water from building up against a basement wall.
25. Stress
• When the deforming force is applied to an object, the object deforms. In order to
bring the object back to the original shape and size, there will be an opposing
force generated inside the object.
• This restoring force will be equal in magnitude and opposite in direction to the
applied deforming force. The measure of this restoring force generated per unit
area of the material is called stress.
• Thus, Stress is defined as “The restoring force per unit area of the material”.
• Denoted by Greek letter σ. Measured using Pascal or N/m2.
• Mathematically expressed as –
Where,
F is the restoring force measured in Newton or N.
A is the area of cross-section measured in m2.
σ is the stress measured using N/m2 or Pa.
26. Strain
• The effect of stress on a body is named as strain
• Strain is the ratio of the amount of deformation experienced by the body in the
direction of force applied to the initial sizes of the body.
• It is expressed in number as it doesn't have any dimensions.
• The relation of deformation in terms of the length of the solid is given below
27. Use of Stress-Strain Graph
• The stress-strain diagram is a graphical representation of the material's strength
and elasticity.
• The stress-strain diagram can also be used to study the behavior of the materials,
which simplifies the application of these materials.
How to Create a Stress-Strain Curve?
• The stress-strain curve is created by progressively adding load to a test coupon
and monitoring the deformation, which allows the stress and strain to be
calculated.
28. Relationship Between Stress and Strain
• Stress and strain have a straight proportional relationship up to an elastic limit.
• The relationship between stress and strain is explained by Hooke's law.
• Hooke's law statesStress and strain have a straight proportional relationship up to
an elastic limit. that the strain in a solid is proportional to the applied stress,
which must be within the solid's elastic limit.
• Hooke’s Law
• When English scientist Robert Hooke was studying springs and elasticity in the
19th century, he observed that numerous materials had a similar feature when
the stress-strain connection was analyzed. Hooke's Law defined a linear zone in
which the force required to stretch material was proportionate to the extension
of the material.
29. Explaining Stress-Strain Graph
The stress-strain diagram has different points or regions as follows:
• Proportional limit
• Elastic limit
• Yield point
• Ultimate stress point
• Fracture or breaking point
30.
31. (i) Proportional Limit
• The region in the stress-strain curve that observes Hooke's Law is known as the
proportional limit.
• According to this limit, the ratio of stress and strain provides us with the
proportionality constant known as young's modulus
(ii) Elastic Limit
• Elastic limit is the maximum stress that a substance can endure before
permanently being deformed.
• When the load acting on the object is completely removed and the material
returns to its original position, that point is known as the object's elastic limit.
32. (iii) Yield Point
• The point at which the material starts showing to deform plastically is known as
the yield point of the material.
• Once the yield point of an object is crossed, plastic deformation occurs. There are
two types of yield points (i) upper yield point (ii) lower yield point.
(iv) Ultimate Stress Point
• The point at which a material endures maximum stress before failure is known as
the Ultimate Stress point. After this point, the material will break.
(v) Fracture or Breaking Point
• In the stress-strain curve, the point at which the failure of the material takes
place is known as the breaking point of the material.
33. Types of Stress
• Stress can be categorized into two categories depending upon the
direction of the deforming forces acting on the body.
34. Normal Stress
• As the name suggests, Stress is said to be Normal stress when the direction of
the deforming force is perpendicular to the cross-sectional area of the body.
• Normal stress can be further classified into two types based on the dimension
of force-
Longitudinal stress
Bulk Stress or Volumetric stress
35. Longitudinal stress
• As the name suggests, when the body is under
longitudinal stress-
• The deforming force will be acting along the length of the body.
• Longitudinal stress results in the change in the length of the body. Hence,
thereby it affects slight change in diameter.
• The Longitudinal Stress either stretches the object or compresses the object
along its length.
• Thus, it can be further classified into two types
based on the direction of deforming force-
Tensile stress
Compressive stress
36.
37. Tensile Stress / Tension
• If the deforming force or applied force results in the increase in the object’s length then
the resulting stress is termed as tensile stress.
• For example: When a rod or wire is stretched by pulling it with equal and opposite
forces (outwards) at both ends.
• Steel is ideally suited to resist tensile stresses and is used widely in construction for this
purpose, for example to reinforce concrete, or in the form of cables, wires and chains.
Compressive Stress / Compression
• If the deforming force or applied force results in the decrease in the object’s
length then the resulting stress is termed as compressive stress.
• For example: When a rod or wire is compressed/squeezed by pushing it with
equal and opposite forces (inwards) at both ends.
• Most materials can carry some compressive stresses ( Ex: Concrete, timber etc.)
other than cables, wires, chains and membranes.
38. Bulk Stress or Volume Stress
• When the deforming force or applied force acts from all dimensions resulting in
the change of volume of the object then such stress in called volumetric stress or
Bulk stress.
• In short, when the volume of body changes due to the deforming force it is
termed as Volume stress.
39. Shearing Stress / Tangential Stress
• When the direction of the deforming force or external force is parallel to the
cross-sectional area, the stress experienced by the object is called shearing
stress or tangential stress.
• This results in the change in the shape of the body.
• Shear stresses make the particles of a material slide relative to each other and
usually result in deformation.
40. Combined Stress
• Most often, a structural member is subjected to different types of stresses that
acts simultaneously.
• Such stresses are axial, shear, flexure, and torsion.
• Superposition method is used to determine the combined effect of two or more
stresses acting over the cross-section of the member.
• Combined stress is defined as any possible combinations of direct stress (tensile,
compressive, shear) and indirect stress (bending, torsional, thermal) developed
inside the body.
Combined Stress = Direct Stress + Indirect Stress
41. Possible combinations are as follows:
1. axial and shear
2. axial and flexural(Bending)
3. axial and torsional
4. torsional and flexural
5. torsional and shear
6. flexural and shear
7. axial, torsional, and flexural
8. axial, torsional, and shear
9. axial, flexural, and shear
10. torsional, flexural, and shear
11. axial, torsional, shear, and flexural
42.
43. Second Moment of Area /Moment of Inertia of a Shape ( I )
• A measure of the 'efficiency' of a shape to resist bending caused by loading.
• It is geometrical property of an area which reflects how its points are distributed
with regard to an arbitrary axis
Second Moment of Area of a
cross-section is found by,
- Taking each mm2 (A) and
multiplying by the square of
the distance ( d
2
) from an axis.
Then add ( ∑) them all up.
46. Bending Moment ( M )
• A bending moment is a force normally measured in a force x length (e.g. kNm)
• Bending moments occur when a force is applied at a given distance away from a
point of reference; causing a bending effect.
• In the most simple terms, a bending moment is basically a force that causes
something to bend.
47. Section modulus (Z)
• Section modulus is a geometric property for a given cross-section used in the
design of beams or flexural members.
• The elastic section modulus is defined as the ratio of the second moment of area
(or moment of inertia) and the distance from the neutral axis to any given (or
extreme) fiber.
• The elastic section modulus is defined as
Z = I / y
here I is the second moment of area (or area moment of inertia)
y is the distance from the neutral axis to any given fibre.
It is often reported using y = c, where c is the distance from the neutral axis to the
most extreme fibre
49. Direct Stress
• Direct Stresses alone is produced in a body when it is subjected to an axial
tensile or compressive load
• Direct Stress produces a change in length in the direction of the Stress.
• Direct stress or simple stress is classified in two type
1. Normal stress – Force acts perpendicular to the surface
Tensile stress
Compressive stress
2. Shear stress – Force acts Tangential to the surface
The stress equation is: σ = F/A.
F denotes the force acting on a body and A denotes the area. Units of stress are
the same as units of pressure - Pascals (symbol: Pa) or Newtons per squared meter.
50. Flexural/Bending Stress
flexural strength
The flexural strength is stress at failure in bending.
It is equal or slightly larger than the failure stress in tension.
• Bending stress is produced in the body when it is subjected to bending
moment(M).
• The Bending stress
σb = + Moment at the section / Section Modulus
σb = + M/Z Where, Z = I/y
σb = + My/I
51. Direct and Bending Stresses
But if a body is subjected to axial loads and bending moments, then both the
stresses will be produced in the body. Therefore,
• The Direct stress (or) Axial stress
σa = Load/ Area
σa =P/A
• The Bending stress
σb = + Moment at the section / Section Modulus
σb = + M/Z
Where e is eccentricity of load P, M is bending moment and Z is the section
modulus about bending axis.
52. Principle of Combined Bending & Direct Stress
• When a column of rectangular section is subjected to an eccentric load the
section is subjected both direct stress and bending stress. the Resultant
stresses due to the combined Bending and Direct Stress are,
σc= σa + σb
σc = P/A + M/Z Where Z = I/y
σc = P/A + My/I
σc = P/A + Mc/I Where y = c
53. Column with Uniaxial Eccentric Loading
• When vertical loads do not
coincide with center of gravity
of column cross section, but
rather act eccentrically either
on X or Y axis of the column
cross section, then it is called
uniaxial eccentric loading
column.
54. Column with Biaxial Eccentric Loading
• When vertical load on the
column is not coincide with
center of gravity of column
cross section and does not
act on either axis (X and Y
axis), then the column is
called biaxial eccentric
loaded column.
55. Combined Bending & Direct Stress Acting on Column Due to
Eccentric Loading
When a column of rectangular section is subjected to an
eccentric load the section is subjected both direct stress
and bending stress. The Resultant stresses due to the
combined Bending and Direct Stress are,
σ = σa + σb
σ = P/A + M/Z
σmax = P/A + M/Z
σmin = P/A - M/Z
59. Scenarios
Conclusion :
Hence for no tensile stress in the section, the direct stress will be greater than or
equal to bending stress.
Scenario Type of Stress
Direct stress is more than
bending stress
σa > σb Then the stress
throughout the section
will be compressive
Direct stress is equal to
bending stress
σa = σb Then the tensile stress
will be zero.
Direct stress is less than
bending stress
σa < σb Then there will be tensile
stress
.
60. Core or Kernel of the section
The core or Kernel of the section is the area with in which the line of action of the
eccentric load may be applied, so as not to produce tensile stress in any part of the
section.
Middle Third Rule for a Rectangular Section
For a rectangular section there will be no tensile stress if the load is on either axis
within the middle third of the section.
61. Derivation of Middle third Rule for Rectangular Area
• The minimum stress (σMin) must be greater or equal to zero for no tensile stress
at any point along the width of the column.
Z = I/eMax
I = bd
3
/12
Assume Bending around x-x,
c = eMax = d/2
c is the distance from the neutral axis
to the most extreme fibre along Y-Y
Z = bd
2
/6
But, A = bd
Z = Ad/6
σmin = P/A - M/Z
σmin > 0
P/A - M/Z > 0
M = Pe
P/A – Pe/ (Ad/6) > 0
P/A - 6Pe/Ad > 0
P/A { 1 – 6e/d } > 0
P/A = 0,
So,
{ 1 – 6e/d } > 0
d/6 > e
62. • Therefore we can say that if load will be applied with an eccentricity equal to or
less than b/6 from the any side of the axis YY then there will not be any tensile
stress developed in the column.
• Hence range within which load could be applied without developing any tensile
stress at any point of the section along the width of the column will be b/3 or
middle third of the base
• Similarly in order to not develop any tensile stress at any point in the section
along the depth of the column, eccentricity of the load must be less than or equal
to (d/6) with respect to axis XX.
• Therefore we can say that if load will be applied with an eccentricity equal to or
less than d/6 from the axis XX and on any side of the axis XX then there will not
be any tensile stress developed in the column.
Derivation of Middle third Rule for Rectangular Area
63. Middle Quarter Rule for Circular Sections
• For a circular section there will be no tensile stress if the load is on either axis
within the a circle of diameter equal to one-forth of the main section diameter
(D/4).
64. Derivation of Middle third Rule for Circular Area
• If load will be applied with an eccentricity equal to or less than d/8 from the axis
XX and on any side of the axis XX then there will not be any tensile stress
developed in the circular section.
• Hence range within which load could be applied without developing any tensile
stress at any point of the section will be d/4 or middle quarter of the main
circular section.
• Area of the circle of diameter d/4 within which load could be applied without
developing any tensile stress at any point of the section will be termed as Kernel
of the section.
