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Important Concepts in Strength of Materials

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  • The property of a material by which it can be drawn into a smaller sections due to tension is called Ductility.

  • The materials which have the same elastic properties in all directions are called Isotropic.

  • The value of Poisson’s ratio always remains – Less than one

  • The minimum number of rivets for the connection of a gusset plate is 2.

  • In a beam the neutral plane – Does not change during deformation

  • For a beam having fixed unknown element of the reactions is – Horizontal and vertical components at both the ends

  • Influence lines are drawn for structures of any type.

  • For a simply supported beam with a central load, the bending moment is maximum at the centre.

  • The equivalent length of a column fixed at one end and free at the other end is 2L

  • The tension coefficient of any member is the tension divided by the length.

  • If a square beam loaded longitudinally, shear develops equally on each fibre along horizontal plane.

  • If the shear force along a section of a beam is zero, the bending moment at the section is Maximum.

  • The shape of the bending moment diagram over the length of a beam carrying a uniformly distributed load is Parabolic.

  • A ductile material has large plastic zone. A brittle material has no plastic zone. A rigid material has no plastic zone.

  • If the width b and depth d of a beam simply supported with a central load are interchanged the deflection at the centre of the beam will be changed in the ratio of – (b/d)2

  • The stress at which extension of a material takes place more quickly as compared to the increase in load is called Yielding point.

  • The number of points of contraflexure in a simple supported beam carrying uniformly distributed load is O.

  • Ties are load carrying members of a frame which are subjected to axial tension loads.

  • At either end of a plane frame maximum number of possible transverse shear forces is one.

  • The cross sections of the beams of equal length are a circle and a square whose permissible bending stress is same under same maximum bending. The ratio of their flexural weights is 1.118.

  • The maximum bending moment due to a moving load on a simply supported beam occurs under the load.

  • If a three hinged parabolic arch carries a uniformly distributed load on its entire span every section of the arch resists – Compressive force

  • In a three hinged arch, the shear force is usually – ‘Maximum at springings

  • A cantilever beam rectangular in cross-section is subjected to an isolated load at its free end. If the width of the beam is doubled, then the deflection of the free end will be changed in the ratio of 1/2.

  • The equivalent length of a column fixed at both ends is 0.5L

  • In a shaft rotated by a couple the Shear forces varies from zero at the centre to a maximum at the circumference.

  • The shape of the bending moment diagram over the length of a beam, carrying a uniformly increasing load is always Cubical.

  • The phenomenon of slow growth of strain under a steady tensile stress is called Creeping.

  • An arch may be subjected to thrust, shear force and bending moment.

  • The law which states, “within elastic limits strain produced is proportional to the stress producing it” is known as Hooke’s Law.

  • When a rectangular beam is loaded longitudinally shear develops on every horizontal plane.

  • The point of contraflexure occurs in – in over hanging beams only.

  • A member which i; subjected to reversible tensile or compressive stress may fail at a stress lower than the ultimate stress of the material. This property of metal is called Fatigue of the metal.

  • The effect of arching a beam is – To reduce the bending moment throughout

  • The under mentioned types are Simple strain, Tensile strain, Compressive strain, Shear strain and Volumetric strain.

  • Hooke’s law States that stress and strain are directly proportional.

  • A column is said to be of medium size if its slenderness ratio is between 32 and 120.

  • The phenomenon of slow extension of materials having constant load, i.e., increasing with the time is called Creeping.

  • The maximum resistance against rotation is offered by the weld at a point most distant.

  • Along the neutral axis of a simply supported beam. fibers do not undergo strain.

  • The distance of the eccentric axial load from the C.G. beyond which tension develops is known as Kerb distance.

  • In visco-elastic material stress-strain relation is dependent on time.

  • An orthotropic material has different properties in three mutually perpendicular directions.

  • A bending moment may be defined as Algebraic Sum of the moments of all the forces on either side of the section.

  • For structural analysis of forces the method refers – Moment-area-theorem

  • The reaction at the supports will be vertical to the plane of the support if the frame structure rests on 1. Roller supports, 2.Free supports, 3.Hinged supports

  • Along the principal plan subjected to maximum principal stress no shear stress acts.

  • A diagram which shows the variations of the axial load for all sections of the span of a beam is called Thrust diagram.

  • In a three hinged arch the third hinge is generally kept at crown of the arch.

  • Stress in members of statically determinate simple frames, can be determined by Method of joints, Method of sections and Graphical solution.

  • The property of a material by which it can be beaten or rolled into thin plates is called Malleability.

  • If a constant section beam is subjected to a uniform bending moment throughout, its length bends too circular arc.

  • The shear force on a simply supported beam is proportional to Algebraic sum of the transverse forces of the section.

  • An arch with three hinges is a structure Statically determinate.

  • At either end of a plane frame maximum number of possible bending moments is Zero.

  • During a tensile test on a ductile material – True stress at fracture is higher than the ultimate stress

  • The type of butt joints in common use is single inverted V-butt joint.

  • A cylinder is said to be thin if the ratio of its thickness and diameter is less than 1/10.

  • Rankine-Golden formula accounts for direct as well as buckling Stress and is applicable to intermediate columns.

  • The point through which the resultant of the shear stresses passes is known as Shear centre.

  • In the standard rolled channels the shear centre is on the horizontal line passing through and away from the C.G. beyond web.

  • In equal angles the shear centre is on the horizontal plane and away from the C.G. outside of the leg projection.

  • In T-sections the shear centre is at the C.G. of the section.

  • For structural analysis Maxwell’s reciprocal theorem can be applied to Elastic structures.

  • The moment diagram for a cantilever carrying a concentrated load at its free end will be triangle.

  • In a three hinged arch the bending moment will be zero at all the three hinges.

  • The ratio of the tensile stress developed in the wall of a boiler in the circumferential direction to the tensile stress in the axial direction is 2.

  • In a shaft the shear stress intensity at a point is not inversely proportional to the distance from the axis.

  • A member which does not regain its original shape after removed of load producing deformation is said to be Plastic.

  • The bending moment is maximum on a section where shearing force changes sign.

  • As the elastic limit reaches, tensile strain increases more rapidly.

  • A member is balanced at its end by two inclined members carrying equal forces, For equilibrium the angle between the inclined bars must be 120 degrees.

  • When a rectangular beam is loaded transversely, the maximum compressive stress develops on top fibre.

  • The rate of change of bending moment is equal to rate of shear force.

  • Failure of riveted joints is due to – 1. Tearing of the plates between the rivet hole and the edge of the plate, 2.Tearing of plates between rivets, 3.Shearing of rivets, 4.Crushing of rivets.

  • The assumptions of the theory of simple bending are – 1.The value of the Young’s modulus is the same in tension as well as in compression, 2.Transverse section of a beam remains plane before and after bending, 3.The material of the beam is homogeneous and isotropic, 4.The resultant pull or thrust on transverse section of a beam is zero.

  • The weakest section of a diamond riveting is the section which passes through first row.

  • In a loaded beam the point of contraflexure occurs at a section where bending moment is. zero or changes sign.

  • The cross-sectional area of the welded member is effective, A welded joint develops strength of its parent metal, Welded joints provide rigidity, Welded joints have better finish.

  • The neutral axis of a beam cross—section must pass through the centroid of the section.

  • The assumption in the theory of pure torsion are – 1.The twist along the shaft is uniform 2. The shaft is uniform circular section throughout, 3.Cross-section of the Shaft which is plane before twist remains plane after twist.

  • The ratio of the effective length of column and minimum radius of gyration of its cross sectional area is known as slenderness ratio.

  • In a solid arch shear force acts perpendicular to the axis of arch.

  • A three-hinged arch is said to be Statically determinate structure.

  • The shape of the bending moment diagram over the length of a beam having no external load is always Linear.

  • For keeping the stress wholly compressive, the load may be applied on a circular column , anywhere within a concentric circle of diameter d/4.

  • If the Stress produced by a prismatic bar is equal to the working stress the area of the cross-section of the prismatic bar becomes infinite.

  • The section modulus of a rectangular section is proportional to area of the section.

  • In a continuous bending moment curve, the point where it changes sign is called – 1.Point of inflexion, 2.Point of contraflexure, 3.Point of virtual hinge.

  • A long vertical member Subjected to an axial compressive load is called Column.

  • The property by which a body returns to its original shape after removal of the force is called Elasticity.

  • For a beam of uniform strength keeping its depth constant, the width will vary in proportion to Bending moment (M).

  • The stress necessary to initiate yielding, is considerably more than that necessary to continue it.

  • Strain energy of any member may be defined as work done on it 1.To deform it, 2.To resist elongation, 3.To resist shortening.

  • When two plates butt together and riveted with two cover plates with two rows of rivets the joint is known as Double riveted double cover butt joint.

  • The moment diagram for a cantilever whose free end is subjected to a bending moment will be a rectangle.

  • Reactions at the supports of a structure can be determined by equating the algebraic sum of – 1.Horizontal forces to zero, 2.Vertical forces to zero, 3.Moment about any point to zero.

  • Shear force for a cantilever carrying a uniformly distributed load over its length is rectangle.

  • If the width of a simply supported beam carrying an isolated load at its centre is doubled then deflection of the beam at the centre is changed by 8 times.

  • Columns of given length, cross-section and material have different values of buckling loads for different end conditions. The strongest column is one whose both the ends are fixed.

  • Every material obeys the Hooke’s law within its Limit of Proportionality.

  • The moment diagram for a cantilever which is subjected to a uniformly distributed load will be a parabola.

  • The areas of cross-section of a square beam and a circular beam subjected to equal bending moments are same. Then square beam is more economical.

  • When equal and opposite forces applied to a body tend to elongate it the stress so produced is called Tensile Stress.

  • Stress in a beam due to Simple bending is directly proportional.

  • For a beam if fundamental equations of statics are not sufficient to determine all the reactive forces at the supports the structure is said to be Statically Indeterminate.

  • The moment diagram for a cantilever carrying linearly varying load from zero at its free end and to maximum at the fixed end will be a cubic parabola.

  • Struts are load carrying members of a frame structure which are subjected to axial compressive loads.

  • A beam is Said to be of uniform strength if bending stress is same at every section along its longitudinal axis.

  • When loads are applied proportionately to a frame structure containing its members in one plane, the structure is called space frame.

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