mcqs – Shear stresses in beams Keywords: shear stress variation- maximum to average ratio-location of maximum and minimum shear stress-distortion Abstract Shear stress in a beam varies parabolically. It is maximum at the centroidal axis and is zero on the outermost fibers. It is quite contrary to bending stress. The direction of shear stress in […]
Spherical thin shell Keywords:Hoop stress, Radial stress, advantages and disadvantages of spherical over cylindrical Various stresses in a thin spherical shell Hoop stress or Tangential stress or Circumferential stress(σh)———-It acts in the tangential direction at the point of consideration Hoop stress or Tangential stress or Circumferential stress(σh)———-It acts in the tangential direction at the point […]
THIN CYLINDRICAL SHELL Keywords: Hoop stress, Longitudinal stress and Radial stress Thin shell A vessel is a thin if its thickness is less as compared to its diameter. Mathematically it is expressed as a thin shell if D/t A vessel is a thin shell where stresses are assumed to be uniform. Uniform stresses mean stress at […]
Thick Cylindrical vessel-3 Keywords: hoop shrinking-pre-stressing, Fabrication stresses Stress AB = –2psr22/ (r22 –r12) compressive Stress CD = ps(r32+r22)/ (r32 –r22) Tensile Stress AA’ = p((r32+r12)/ (r32 –r12) Stress CC’ = pr12((r32+r22)/[r22(r32 –r12)] Final stress at A = AA’ – AB=p((r32+r12)/ (r32 […]
Radial deflection-thick shell Keywords: Hoop shrinking, shrinkage pressure, Pre-stresses, Circumferential strain Hot Outer cylinder (called the jacket with radii as r2 and r3) is put on to the inner cylinder (with radii as r1 and r2) and is allowed to cool. A pressure will be developed both on the jacket and the cylinder. Let ps […]
Thick Cylindrical Shell-2 Keywords: Internal pressure- external pressure- hoop shrinking 1. Only internal pressure pi is there and po =0 σhmax = [pi(ri2+ro2]/ (ro2 –ri2) σhmax > pi σr max = pi σhmax > σr max Both σhmax and σr max occur at the innermost radius and σhmax is always greater than the σr […]
Lame’s equations Keywords: circumferential stress-longitudinal stress-radial stress Lame’s Equations are σh = β/r2 + α σr = β/r2 – α Where α and β are Lame’s constants There is a thick vessel subjected to internal fluid pressure pi at the inner radius ri and external fluid pressure po at the outer radius ro respectively. We […]
Thick shell-1 Keywords: Hoop stress- radial stress-longitudinal stress Stresses in a thin shell were uniform whereas stresses in a thick shell are variable. Interest lies in the determination of maximum stresses and their location. We have already learnt about thin shells where stresses were assumed to be uniform in the thickness of the vessel. i.e. […]
Middle -third rule- Middle-quarter rule: Brittle materials – eccentric loading Keywords: Middle -third rule and Middle-quarter rule- eccentricity-rectangular-circular sections Abstract There are numerous applications where combined bending and axial loading is found. For example: industrial chimney, Dam, All buildings and structures, all poles and trees. In all these applications, self weight is the axial compression load […]
moment of inertia Keywords: Centroid-Neutral axis-Second moment of the area Definition: It is a property of a cross-sectional area to resist bending. Larger is the value of moment of inertia, lesser will be the bending. It is also called second moment of the area of cross-section. Symbol Its symbol is ‘I’. Units Its unit is mm4. […]