Lab Session No. 03
Objective:
To find out the modulus of rigidity of
rubber block using Rubber shearing Apparatus
Ø Rubber Shearing Apparatus
Ø Dial gauge
Ø Weights and hanger
Ø Meter Rod
Procedure:
1.
First of all, set the dial
gauge at zero.
2.
Loads of different magnitudes are successively
applied to the hangers and record the readings of vertical deflection in the
rubber by dial gauge.
3.
Repeat the experiment for
increasing load and record the vertical displacement of rubber block in each
case.
4.
Unload and note the
corresponding reading with the decreasing load.
5.
Calculate the modulus of
rigidity of rubber.
Description
Shear Stress
The intensity of force acting tangent to ∆A is called the shear stress,
t (tau). Here we have two shear stress components,
The subscript notation z specifies the orientation of the area ∆A, Fig., and x and y indicate the axes along which each shear stress acts.
Shear Strain
Deformations not only cause line segments to elongate or
contract, but they also cause them to change direction. If we select two line
segments that are originally perpendicular to one another, then the change in
angle that occurs between them is referred to as shear strain. This angle is
denoted by g (gamma) and is always measured in radians (rad),which are
dimensionless. For example, consider the two perpendicular line segments at a
point in the block shown in Fig. 2–3a. If an applied loading causes the block
to deform as shown in Fig. 2–3b, so that the angle between the line segments
becomes u, then the shear strain at the point becomes
Notice that if θ is smaller than π/2 then
the shear strain is positive, whereas if θ is larger than π/2, then the shear strain
is negative.
engineers use a specimen in the shape of a thin tube and subject it to a torsional loading. If measurements are made of the applied torque and the resulting angle of twist, the data can be used to determine the shear stress and shear strain within the tube and thereby produce a shear stress–strain diagram such as shown in Fig. Like the tension test, this material when subjected to shear will exhibit linear elastic behaviour and it will have a defined proportional limit τpl. Also, strain hardening will occur until an ultimate shear stress τu is reached. And finally, the material will begin to lose its shear strength until it reaches a point where it fractures, τf. For most engineering materials, like the one just described, the elastic behaviour is linear, and so Hooke’s law for shear can be written as
Here G is called the shear modulus of elasticity or the modulus of rigidity. Its value represents the slope of the line on the t–g diagram, that is, G = τpl./ γpl. Units of measurement for G will be the same as those for τ (Pa or psi), since g is measured in radians, a dimensionless Quantity
Observations and Calculations:
Shear Stress(τ)=F/(l*t)
Shear Strain(γ)=δs/w
Modulus of Rigidity(G)=τ/γ=Fw/tlδs
Length of Rubber Block (l) =
Length of Rubber Block (w) =
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