The wire in figure 1 is pulled by the action of a mass attached to its lower end. In this condition the wire is in tension. Suppose the total load on the cross-section of the wire is P and the cross-sectional area of the wire is A, then the uniform tensile stress () in the(…)
Solid Mechanics
COMBINED BENDING, DIRECT AND TORSIONAL STRESSES
COMBINED BENDING, DIRECT AND TORSIONAL STRESSES IN SHAFTS Cases arise such as in propeller shafts of ships where a shaft is subjected to direct thrust in addition to bending moment and torsion. In such cases the direct stresses due to bending moment and the axial thrust have to be combined into a single resultant. a)(…)
TORSION OF SHAFTS
When a cylindrical shaft is subjected to equal and opposite couples at the ends, either it will be in equilibrium or it will rotate at a uniform rate. In either case, it is subjected to torsion and the stresses set up by every cross-section are shear stresses. At any point in the cross-section of a(…)
SHEAR CENTRE -WITH EXAMPLES
If a beam is subjected to bending moments and shear force in a plane, other than the plane of geometry, which passes through the centroid of the section, then bending moment will be accompanied by twisting. In order to avoid twisting and cause bending only, the transverse forces must act through a point which may(…)
THEORY OF SIMPLE BENDING
Assumptions: Plane sections of the beam, originally plane, remain plane. The material of the beam is homogeneous and obeys Hooke’s law. The moduli of elasticity for tension and compression are equal. The beam is initially straight and of constant cross-section. The plane of loading must contain a principle axis of the beam cross-section and the(…)
FLITCHED BEAMS
Beams that are built of more than one material are called composite beams. Examples are bimetallic beams, which consists of two different metals bonded together, sandwich beams, and reinforced concrete beams. Composite beams may be analysed by the same bending theory as used for the analysis of ordinary beams, because the assumption that the cross-section(…)
DETERMINATE AND INDETERMINATE STRUCTURES
Structure is an assemblage of a number of components like slabs, beams, columns, walls, foundations and so on, which remains in equilibrium. It has to satisfy the fundamental criteria of strength, stiffness, economy, durability and compatibility, for its existence. It is generally classified into two categories as Determinate and Indeterminate structures or Redundant Structures. Any(…)