18ENG25: BUILDING STRUCTURES-II
CONTACT PERIODS: 3 (1 LECTURE + 2 PRACT./TUTORIAL/SEMINARS) PER WEEK
THEORY MARKS: 100
PROGRESSIVE MARKS : 50
DURATION OF EXAM : 3 HRS
OBJECTIVE: INTRODUCTION TO MECHANICS & MATERIALS.
LEARNING OUTCOME: At the end of the course the students will have the ability to
understand the effect of forces on deformable bodies.
REFERENCES:
1) B.S.Basavarajaih & P. Mahadevappa, "Strength of Materials", Universities Press, 3rd
editn. 2010.
2) Dr. S. Ramamrutham & R. Narayan "Strength of Materials", Dhanpat Rai Publ., 8th
edition.
2014.
3) William A. Nash, "Strength of Materials", McGraw-Hill Education; 6th edition, 2013.
4) R.K.Bansal, "Strength of Materials", Laxmi Publications; 6th edition (2017).
5) R.S.Khurmi & N. Khurmi, " Strength of Materials", S Chand Pub., revised edition
2006.
Every material is elastic in nature. That is why whenever some external
system of forces acts on a body, it undergoes some deformation. As the
body undergoes deformation, its molecules set up some resistance to
deformation. This resistance per unit area to deformation is known as
stress.
Mathematically stress may be defined as the force per unit area,
σ = P/A
P = Load or force acting on the body
A = Cross-sectional area of the body
In S.I system, the unit of stress is Pascal(Pa) (same as that of pressure)
which is equal to N/m2
When a single force or a system of forces acts on a body, it undergoes
some deformation. This deformation per unit length is known as Strain.
Mathematically strain may be defined as the deformation per unit
length,
ε = δl/l
δl = Change in length of the body
l = Original length of the body
HOOKE’S LAW
The law is named after 17th
century British physicist Robert Hooke. He first stated
the law in 1676 as a Latin anagram. He published the solution of his anagram as:
ut tension, sic vis (“as the extension, so the force”)
The Hooke’s law states that “When a material is loaded, within
its elastic limit, the stress is proportional to the strain”
Mathematically,
Stress/Strain = E = Constant
It may be noted that Hooke’s law holds good for tension as well
as compression.
FACTOR OF SAFETY
A Factor of safety (FoS), also known as (and used interchangeably
with) Safety factor (SF), expresses how much stronger a system is than
it needs to be for an intended load. Safety factors are often calculated
using detailed analysis because comprehensive testing is impractical
on many projects, such as bridges and buildings, but the structure's
ability to carry a load must be determined to a reasonable accuracy.
Many systems are intentionally built much stronger than needed for
normal usage to allow for emergency situations, unexpected loads,
misuse, or degradation (reliability).
The definition for the factor of safety (FoS):
The ratio of a structure's absolute strength (structural capability) to actual applied
load.
STRESS-STRAIN CURVE FOR MILD STEEL
STRESS-STRAIN CURVE FOR HIGH STRENGTH STEEL
When a body is subjected to direct tensile or compressive
stress, an axial deformation of the body takes place. At
the same time there will be lateral or side effects of
pushes and pulls. The axial strain of a body is always
followed by an opposite kind of strain in all directions at
right angle to it.
In general there are 2 types of strains in a body when
subjected to a direct stress:
• Primary or Linear strain
• Secondary or Lateral strain
• Linear Strain: The deformation of the bar per unit
length in the direction of force, (δl/l)
• Lateral Strain: The strain in the direction at right angles
to it. (d±δd)
POISSON’S RATIO
It has been experimentally found, that if a body is stressed within
its elastic limit, the lateral strain bears a constant ratio to the linear
strain.
Mathematically;
Lateral strain/Linear strain = constant
This constant is known as Poisson’s ratio and is denoted by 1/m or µ
Lateral strain = (1/m) x ε = µε
RELATIONSHIP BETWEEN ELASTIC CONSTANTS
• Modulus of Elasticity or Young’s Modulus, E = σ/ε
• Bulk Modulus, K = σ/(δV/V)
• Relation between K and E : K = mE/3(m-2)
• Shear Modulus or Modulus of rigidity, C = τ/φ
• Relation between E & C : C = mE/2(m+1)
Whenever there is some increase or decrease in the
temperature of a body, it causes the body to expand or
contract. If body is allowed to expand or contract freely,
with the rise and fall of temperature, no stresses are
induce in the body. But if the deformation of the body if
prevented, some stresses are induced in the body. Such
stresses are called thermal stresses or temperature
stresses. The corresponding strain are called thermal
strains or temperature strains.
THERMAL STRESSES IN SIMPLE BARS
The thermal stresses or strains may be found out by finding amount of
deformation due to change in temperature, then by finding thermal
strain due to deformation. The thermal stress may be found from
thermal strain as usual. Now consider a body subjected to an increase in
temperature.
Then increase in length due to increase in temperature is, δl = l.α.t
l = original length of the body
t = Increase of temperature
α = Coefficient of linear expansion
If the ends of the bar are fixed to rigid supports, so that
its expansion is prevented, then compressive strain
induced in the bar,
ε = δl/l = l.α.t/l = α.t
Therefore, Stress σ = ε.E = α.t.E

BUILDING STRUCTURE 1 (MODULE 1) ARCHITECTURE

  • 1.
    18ENG25: BUILDING STRUCTURES-II CONTACTPERIODS: 3 (1 LECTURE + 2 PRACT./TUTORIAL/SEMINARS) PER WEEK THEORY MARKS: 100 PROGRESSIVE MARKS : 50 DURATION OF EXAM : 3 HRS OBJECTIVE: INTRODUCTION TO MECHANICS & MATERIALS.
  • 2.
    LEARNING OUTCOME: Atthe end of the course the students will have the ability to understand the effect of forces on deformable bodies. REFERENCES: 1) B.S.Basavarajaih & P. Mahadevappa, "Strength of Materials", Universities Press, 3rd editn. 2010. 2) Dr. S. Ramamrutham & R. Narayan "Strength of Materials", Dhanpat Rai Publ., 8th edition. 2014. 3) William A. Nash, "Strength of Materials", McGraw-Hill Education; 6th edition, 2013. 4) R.K.Bansal, "Strength of Materials", Laxmi Publications; 6th edition (2017). 5) R.S.Khurmi & N. Khurmi, " Strength of Materials", S Chand Pub., revised edition 2006.
  • 8.
    Every material iselastic in nature. That is why whenever some external system of forces acts on a body, it undergoes some deformation. As the body undergoes deformation, its molecules set up some resistance to deformation. This resistance per unit area to deformation is known as stress. Mathematically stress may be defined as the force per unit area, σ = P/A P = Load or force acting on the body A = Cross-sectional area of the body In S.I system, the unit of stress is Pascal(Pa) (same as that of pressure) which is equal to N/m2
  • 17.
    When a singleforce or a system of forces acts on a body, it undergoes some deformation. This deformation per unit length is known as Strain. Mathematically strain may be defined as the deformation per unit length, ε = δl/l δl = Change in length of the body l = Original length of the body
  • 23.
    HOOKE’S LAW The lawis named after 17th century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram. He published the solution of his anagram as: ut tension, sic vis (“as the extension, so the force”)
  • 24.
    The Hooke’s lawstates that “When a material is loaded, within its elastic limit, the stress is proportional to the strain” Mathematically, Stress/Strain = E = Constant It may be noted that Hooke’s law holds good for tension as well as compression.
  • 25.
    FACTOR OF SAFETY AFactor of safety (FoS), also known as (and used interchangeably with) Safety factor (SF), expresses how much stronger a system is than it needs to be for an intended load. Safety factors are often calculated using detailed analysis because comprehensive testing is impractical on many projects, such as bridges and buildings, but the structure's ability to carry a load must be determined to a reasonable accuracy. Many systems are intentionally built much stronger than needed for normal usage to allow for emergency situations, unexpected loads, misuse, or degradation (reliability).
  • 26.
    The definition forthe factor of safety (FoS): The ratio of a structure's absolute strength (structural capability) to actual applied load.
  • 28.
  • 38.
    STRESS-STRAIN CURVE FORHIGH STRENGTH STEEL
  • 39.
    When a bodyis subjected to direct tensile or compressive stress, an axial deformation of the body takes place. At the same time there will be lateral or side effects of pushes and pulls. The axial strain of a body is always followed by an opposite kind of strain in all directions at right angle to it. In general there are 2 types of strains in a body when subjected to a direct stress: • Primary or Linear strain • Secondary or Lateral strain
  • 40.
    • Linear Strain:The deformation of the bar per unit length in the direction of force, (δl/l) • Lateral Strain: The strain in the direction at right angles to it. (d±δd)
  • 41.
    POISSON’S RATIO It hasbeen experimentally found, that if a body is stressed within its elastic limit, the lateral strain bears a constant ratio to the linear strain. Mathematically; Lateral strain/Linear strain = constant This constant is known as Poisson’s ratio and is denoted by 1/m or µ Lateral strain = (1/m) x ε = µε
  • 46.
    RELATIONSHIP BETWEEN ELASTICCONSTANTS • Modulus of Elasticity or Young’s Modulus, E = σ/ε • Bulk Modulus, K = σ/(δV/V) • Relation between K and E : K = mE/3(m-2) • Shear Modulus or Modulus of rigidity, C = τ/φ • Relation between E & C : C = mE/2(m+1)
  • 54.
    Whenever there issome increase or decrease in the temperature of a body, it causes the body to expand or contract. If body is allowed to expand or contract freely, with the rise and fall of temperature, no stresses are induce in the body. But if the deformation of the body if prevented, some stresses are induced in the body. Such stresses are called thermal stresses or temperature stresses. The corresponding strain are called thermal strains or temperature strains.
  • 55.
    THERMAL STRESSES INSIMPLE BARS The thermal stresses or strains may be found out by finding amount of deformation due to change in temperature, then by finding thermal strain due to deformation. The thermal stress may be found from thermal strain as usual. Now consider a body subjected to an increase in temperature. Then increase in length due to increase in temperature is, δl = l.α.t l = original length of the body t = Increase of temperature α = Coefficient of linear expansion
  • 56.
    If the endsof the bar are fixed to rigid supports, so that its expansion is prevented, then compressive strain induced in the bar, ε = δl/l = l.α.t/l = α.t Therefore, Stress σ = ε.E = α.t.E