a) Pressure vessels are closed structures containing liquids or gases under pressure.These are special case of plane stress i.e. b) When pressure vessels have walls that are thin in comparison to their overall dimensions, they are included within a more general category known as shell structures. c) Pressure vessels are considered to be thin-walled when the ratio of radius r to wall thickness t is greater than 10 …
a) Euler formula is valid for Long columns only a) For short and intermediate columns and empirical formula which is applicable to all kind of columns was experimentally find out by Rankine Alternative form of Rankine Gordon formulae
a) The critical loads for columns with various kinds of support conditions can be determined from the differential equation of the deflection curve by following the same procedure as above Step 1 With the column assumed to be in the buckled state, we obtain an expression for the bending moment in the column. Step 2 Set up the differential equation of the…
b) Here y-axis is positive towards left and deflection v is positive towards left side b) From equilibrium of moments about point A, we obtain From above two equations we will get Therefore final equation is General solution Value of constants is found out from boundary condition which in this case is basically end conditions. Buckling of pinned-end column in the…
and from diagram we can say that total rotation is 2θ then the restoring moment iii) Taking Moment equilibrium at point B From above equation we will get one trivial solution and second solution gives us the critical load At the critical value of the load the structure is in equilibrium regardless of the magnitude of the angle …
a) If a compression member is relatively slender, it may deflect laterally and fail by bending rather than failing by direct compression of the material. b) When lateral bending occurs, we say that the column has buckled. Under an increasing axial load, the lateral deflections will increase too, and eventually the column will collapse completely.
a.)Macaulay functions are used to represent quantities that “begin” at some particular point on the x-axis and have the value zero to the left of that point. Some of the basic algebraic operations, such as addition, subtraction, and multiplication by a constant, can be performed on the Macaulay functions. Few examples of Macaulay function b.)How…
a.)First Moment-Area Theorem The angle between the tangents, denoted, is equal to the difference between and First moment-area theorem: The angle between the tangents to the deflection curve at two points A and B is equal to the area of the M/EI diagram between those points. b.)Second Moment-Area Theorem Second moment-area theorem: The tangential deviation of point B from the tangent…
a.) To obtain the equation of the deflection curve, we must express the deflection vas a function of the coordinate x. b.) When the beam is bent, there is not only a deflection at each point along the axis but also a rotation. The angle of rotation θ (angle of inclination or angle of slope) of the axis of the…
a) When a beam with a straight longitudinal axis is loaded by lateral forces, the axis is deformed into a curve, called the deflection curve of the beam. b) Most procedures for finding beam deflections are based on the differential equations of the deflection curve and their associated relationships. c) Consider a cantilever beam with a concentrated load…