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The resistance per unit area, offered by a body against deformation is known as:
Which of the following load does not act on the considerable length of the beam?
Point load is that load which acts over a small distance. Because of concentration over small distance this load can may be considered as acting on a point. Point load is denoted by P and symbol of point load is arrow heading downward (↓).
Uniformly distributed load is that whose magnitude remains uniform throughout the length.
Uniformly Varying Load (Non – Uniformly Distributed Load): It is that load whose magnitude varies along the loading length with a constant rate.
Uniformly varying load is further divided into two types:
Shear stress on a beam section is:
(i) Zero at extreme fibres
(ii) Maximum at neutral axis
. Maximum Principal stress theory was postulated by Rankine. It is suitable for brittle materials.
2. Maximum Principal strain theory was postulated by St Venant. This theory is not accurate for brittle and ductile materials both.
3. Maximum Shear stress theory was postulated by Tresca. This theory is suitable for ductile materials. Its results are the safest.
4. Maximum shear strain energy theory was postulated by Vonmises. Its results in case of pure shear are the accurate for ductile materials.
The maximum deflection due to a load W at the free end of a cantilever of length L and having flexural rigidity EI is
The maximum deflection will occur at
If section modulus of a beam is increased, the bending stress in the beam will:
Bending Moment Equation
For the constant bending moment: σ ∝ 1/Z
So, bending stress is inversely proportional to the Section Modulus 'YH
When the shear force diagram is a parabolic curve between two points, it indicates that there is a
The general relationship between the shear force diagram, bending moment diagram and loading diagram will be:
1. Shear force diagram is 1^{o} higher than loading diagram.
2. Bending moment diagram is 1^{o }higher than shear force diagram.
3. For the uniformly varying load on the beam, the shear force diagram is parabolic in nature.
4. For the uniformly varying load on the beam, the bending moment diagram is also parabolic but is 1^{o} higher than shear force diagram.
Mohr’s circle can be used to determine the following stress on an inclined surface:
A. Principal stress
B. Normal stress
C. Tangential stress
D. Maximum shear stress
Mohr circle is a graphical representation of plane stress which helps in determining the relationships between normal and shear stresses acting on any inclined plane at a point in a stressed body.
Mohr’s circle of stresses is a graphical method of finding normal, tangential and resultant stresses on an oblique plane.
The ratio of moment of inertia of circular plate to that of square plate of equal depth is:
Moment of inertia (I_{1}) of circular plate of diameter “D” is given by:
.
Moment of inertia (I_{2}) of square plate of side equal to diameter “D” of circular plate is given by:
Elastic Rubber: 0.5
Wood: Because wood is orthotropic, 12 constants are required to describe elastic behaviour: 3 moduli of elasticity, 3 moduli of rigidity, and 6 Poisson’s ratios (vary from 0.02 to 0.47). These elastic constants vary within and among species and with moisture content and specific gravity.
Copper: 0.33
Steel: 0.27  0.30
The major and minor principal stresses at a point are 3Mpa and 3Mpa respectively. The maximum shear stress at the point is
Maximum shear stress (τ) is given by:
The equivalent length of a column of length L having one end fixed and the other end free is
Effective length of columns under different end conditions are:
1. For both ends hinged: L_{e} = L
2. One end fixed and another end free: L_{e} = 2L
3. Both ends fixed = Le=
4. One end fixed and other is hinges: Le=
The radius of Mohr’s circle for two equal and unlike principal stresses of magnitude “p” is:
Radius of Mohr’s circle is given by:
r=
At principal plane, σ_{x} = σ_{1}, σ_{y} = σ_{2}
τ_{xy} = 0
r=
σ_{1 }= p , σ_{2} = p
r=
r = p
A rectangular beam is 24 cm wide and 50 cm deep, its section modulus is given by:
Section modulus is defined as the ratio of moment of inertia of a beam about its C.G to the maximum distance of extreme xsection of the beam (Y_{max}).
The stress at a point in a bar is 200 MPa tensile. Determine the intensity of maximum shear stress in the material.
Stress on x face, A(200, 0) and Stress on y face, B(0, 0)
Maximum shear stress = Radius of Mohr circle
τ_{max}= σ/2 = 100 MPa
The correct relation between Modulus of elasticity (E), Shear Modulus (G) and Bulk modulus (K) is:
Relation between Modulus of elasticity (E), Shear Modulus (G) and Bulk modulus (K) is given by:
Now, rewriting the equation as follows:
3KE + GE = 9KG
3KE – 9KG =  GE
K(3E – 9G) =  GE
The total area under the stressstrain curve of a mild steel specimen tested up to failure under tension is a measure of its:
Strength is defined as the ability of the material to resist, without rupture, external forces causing various types of stresses. Breaking strength is the ability of a material to withstand a pulling or tensile force.
Toughness is defined as the ability of the material to absorb energy before fracture takes place. In other words, toughness is the energy for failure by fracture. Toughness is measured by a quantity called modulus of toughness. Modulus of toughness is the total area under a stressstrain curve in tension test, which also represents the work done to fracture the specimen.
Hardness is defined as the resistance of a material to penetration or permanent deformation. It usually indicates resistance to abrasion, scratching, cutting or shaping.
Stiffness or rigidity is defined as the ability of the material to resist deformation under the action of external load. Modulus of elasticity is the measure of stiffness.
Limit of poisons ratio varies between 1 to 0.5.
μ = 0.5 for rubber.
Slenderness ratio ( λ ) of long column is defined as the ratio of Effective length of column to its least radius of gyration.
The neutral axis of a beam is subjected to _________ stress.
The neutral axis is an axis in the crosssection of a beam (a member resisting bending) or shaft along which there are no longitudinal stresses or strains. If the section is symmetric, isotropic and is not curved before a bend occurs, then the neutral axis is at the geometric centroid. All fibers on one side of the neutral axis are in a state of tension, while those on the opposite side are in compression.
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