mcqs – Shear stresses in beams The direction of shear stress in a loaded beam is (a) Horizontal (b) Horizontal as well as vertical (c) Vertical (d) None (Ans: b) Shear stress in the beam acting on the cross section is (a) Normal to the cross section (b) Tangential to the cross section (c) Neither normal […]

 Thin spherical shell  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 of consideration Radial stress(σr)———-It acts in the radial direction at the point […]

THIN CYLINDRICAL SHELL 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 the inner to outer radius is of […]

Thick Cylindrical  vessel-3 Pre-stresses Refer to Fig. below: Fig. Pre-stresses                       Fig. Resultant stress variation PRE-STRESSES (due to hoop shrinking) Stress AB = –2psr22/ (r22 –r12)  compressive Stress CD = ps(r32+r22)/ (r32 –r22)    Tensile STRESSES DUE TO FLUID PRESSURE Stress AA’ = p((r32+r12)/ (r32 –r12) Stress CC’ = […]

Radial deflection-thick shell Hoop shrinking 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). Then it is allowed to cool. A pressure will be developed both on the jacket and the cylinder. Let ps is the shrinkage pressure developed […]

  Thick Cylindrical Shell-2 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 max. This shown in the Fig. This […]

LAME’S EQUATIONS 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 want to find the equations […]

Thick shell-1 We have already learnt about thin shells where stresses are assumed to be uniform in the thickness of the vessel. i.e. stresses at the inner or outer radius are same. There is no variation of hoop stress, longitudinal stress and radial stress. However when pressure is high, thin walled vessels cannot be used. […]

Middle third rule- Middle quarter rule In such cases, maximum and minimum stresses will co-exist in the outermost fibers. Maximum stress σmax = M/Z + P/A= Maximum compressive Minimum stress σmin = M/Z – P/A+ can be compressive, zero or tensile depending upon the relative magnitude of M/Z and P/A Case 1 If M/Z < P/A, […]

Moment of inertia and Polar moment of inertia 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’. […]