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Showing posts from December, 2019

Elongation of bars due to axial loading

1. Elongation of simple bar    For  prismatic bar area is constant along depth Change in length   ( ΔL) = PL/AE                 Here, P = pull applied                           L = length of section                           A = area of section                           E = Young's modulus of elasticity of material 2. Elongation of stepped bar Elongation (   Δ) =                    (PL 1 /A 1 E) + (PL 2 /A 2 E) + (PL 3 /A 3 E) 3. Elongation of circular tapering bar Elongation (   Δ) = (4PL/ πED 1 D 2 ) 4. Elongation of composite bar Elongation (   Δ) = [PL(A 1 E 1 +A 2 E 2 )]

Euler's Theory of failure : ( BUCKLING FAILURE)

Euler's theory is not valid for short column because in short column, crushing occurs before buckling. For validity of Euler's theory buckling should occur before crushing, it means slenderness ratio should be greater than or equal to critical slenderness ratio. Assumptions: Material is isotropic, homogeneous and linearly elastic in which Hook's law is valid. The plane cross section remains plane before and after of application Column under the analysis is assumed to be a long column. The failure of the column is assumed to be due to buckling. Before loading column is perfectly straight. Weight of column is neglected. The load is perfectly axial and passes through the centroid of the column section  Here, E = Young's modulus           I = minimum moment of inertia about  traverse  axis           L= effective length or equivalent length of column Effective length  is defined as distance between two adjacent points of zero bending moment or contra f

Torsion in shafts

ASSUMPTIONS: The material is isotropic, homogeneous and linearly elastic in which hooks law is valid. The plane section before twisting remains plane even after twisting. It means the radii which are straight before twisting remains straight even after twisting. The section of the shafts is assumed to be circular which may be solid or hollow and area is prismatic. NOTE: If section is non-circular then shear stress distribution will ne non-linear. Hence there may occur warping and plain section may not remain plain. SIGN CONVENTION: The torque is taken as positive which produces +ve shear stress element on the surface of shafts and vice- versa RIGHT HAND THUMB RULE: If right hand direction of torque applied towards the section thr torque is taken +ve. In this table, NA stands for neutral axis Effect of torsion:  Under pure tension, ductile materials fail in shear and failure plane is the plane of maximum shear stress which is at 90° to longitudinal axis. In br

Types of shear failure of foundation of soil

1. General shear failure This type of failure is seen in dense sand or silt or over consolidated clay It always occur in shallow foundation The failure surface develops between the edge of footing and ground surface This failure occur in low compressible soil Tilting of foundation occur in one side only Stress zone will get extend upto ground level The strain develops is less than 5% The relative density or density index  (I D )  is less than 70% The value of   is always less than  36 o   ( >36 o )  The void ratio is less than 0.55 The standard penetration value is greater than 30     2. Local shear failure This type of failure occurs in loose sand and soft clay in shallow footing Stress zone does not reach upto ground surface and little bulging of soil around footing is observed There is no tilting of footing       The failure surface is not well defined The void ratio is greater than 0.75 The standard penetration value is less than 5 The rel

Correction due to curvature and refraction AND combined correction in surveying

In geodetic surveying, error due to curvature and refraction is taken into action when the area is greater than 256 km²   Correction due to curvature (Cc)             Error due to curvature is taken into action because during leveling with theodolite    or Autolevel the horizontal line and level line do not coincide. Level line is curved line parallel to the earth surface and horizontal line is straight line.               this correction is given by Cc =0.07849 d² OR 0.0785d²                                                                 here, d is the linear distance (in km)   Correction due to refraction (Cr)             Error due to refraction is taken into action due to the changing of medium of light either from a denser medium to lightier medium or viceversa.                    it is 1/7 of correction due to curvature                                               1/7x(0.785 d²)                                                   it is equals to 0.112d²          

Tips for shear force and bending moment diagram

For concentrated or point load, SFD is rectangular (uniform) and BMD is triangular (linear). For uniformly distributed load, SFD is triangular and BMD is parabolic. For uniformly varying load, SFD will be parabolic and BMD will be cubic.  If the algebraic sum of moments on the beam is zero and no other forces are acting then reactions are zero and SFD is a straight line. If there is a vertical ordinate or sudden jump in a BMD, it indicates concentrated moment at that point whose magnitude is equals to length of the ordinate. At fixed end, bending moment is always zero, until an concentrated moment not there.