Prof.Kodali Srinivas

                                               1.      What is Slope Deflection Method?(Oct/Nov 2010)           The Slope Deflection  equations gives the moments at end of a member. These are expressed in terms of  the deformations (ie.slopes & displacements). This method is used for the analysis statically indeterminate beams and rigid frames.     2.      What are the assumptions used in the slope deflection method?(Oct/Nov 2010)      1) The method of the structure is linearly elastic.     2) The structure is loaded within the elastic limit of its material and the principle of superposition is also for the analysis.    3) The axial displacements and shear displacements are negligible and they are neglected in the analys...

Most Engineering design is based on the "Elastic Theory of Bending" and the method is to calculate the maximum Stresses which occur, and to then keep them within the working Stresses in both compression and Tension. These working Stresses are calculated from the Yield (or ultimate) Stress and a Factor of Safety.  This approach is a little unrealistic since Mild Steel Structures do not fail when the edge Stress of any cross section reaches the Yield point, and will continue to withstand the load as long as the central core of the section remains within the Elastic State.  Through ductility, structure is able to absorb large deformations beyond elastic limit without the danger of fracture. It is this characteristics feature of steel that makes possible the application of plastic analysis to structural design. Figure 1: Stress strain diagram (for mild steel) Stress-strain diagram for mild steel in tension is shown in figure-1. Let ‘ab’ represent the elastic range, ...

The slope deflection equations express the member end moments in terms of rotation angles and deflections. The slope deflection method is used for analysis of statically indeterminate structures such as beams and frames. This method was  introduced  by Prof.George A. Maney,in 1915. Sign Convention: 1. The clock wise moments,and clock wise rotations/slopes are taken as positive ones. 2. The down ward displacements of the right end with respect to the left end of horizontal  member is considered as positive. 3. The right ward displacement of upper end with respect to lower end of a vertical member is taken as positive.  Assumptions in the slope- deflection method: 1. The material of the structure is linearly elastic. 2. The structure is loaded with in elastic limit. 3. Axial displacements,Shear displacements are neglected. 4. Only flexural deformations are considered The slope deflection equations of member AB of flexural rigi...

A structural member loaded axially in compression is generally called a compression member. Vertical compression members in buildings are called columns, posts or stanchions. A compression member in roof trusses is called struts and in a crane is called a boom. If the load on a column is applied through the center of gravity of its cross section, it is called an  'axial load' . A load at any other point in the cross section is known as an eccentric load.  As the axial load on a perfectly straight slender column with elastic material properties is increased in magnitude, this ideal column passes through three states: a)Stable equilibrium :     The straight column under load is in stable equilibrium if a lateral force, applied between the two ends of the column, produces a small lateral deflection which disappears and the column returns to its straight form when the lateral force is removed. b)Neutral equilibrium : If the colum...

A  cable  is most often two or more wire  running side by side and bonded, twisted or braided together to form a single assembly.  Cables  are used for lifting, hauling and towing or conveying force through tension.  Cables are commonly used to support suspension bridges, as permanent guys for transmission towers, chimneys and building roofs. Analysis of cables : Cables are perfectly flexible members which are assumed to have no flexural strength. They carry loads by simple tension. The reactions at supports (Ra,Ha,Rb,Hb) will be calculated by using three static equations and forth equation is obtained from consideration that the Bending moment at any point in the cable is zero. Shape of the cable:   Cable subjected to concentrated loads, will take the shape of funicular polygon .  cables - parabolic shape   If it is loaded with uniform distributed load along the horizontal span, it will take t...

The arch is one of the oldest structures. The Romans developed the semi circular true masonry arch.which they used extensively in both bridges and aqueducts.  An arch is a curved beam in elevation. The horizontal moment at the supports is wholly or partially prevented in arches. Hence a horizontal thrust induced at the supports. The supports must effectively arrest displacements in the vertical and horizontal directions in the arch action. Types of Arches Based on their geometry, arches can be classified as semicircular, segmental, or pointed. Based on the number of internal hinges, they can be further classified as two-hinged arches, three-hinged arches, or fixed arches.  An arch with a hinge at each support and third hing at the high point / crown or any where in the rib of arch is known as Three Hinged Arch . An arch with a hinge at each support and no hinge exists anywhere in the rib, it will called as a Two-hinged arch. An arch without hinges at  supports and...

Analysis of multi-storey building frames involves lot of complications and tedious calculations by using conventional methods. To carry out exact analysis is a time consuming task. Substitute frame method for analysis of multistory frame can be handy in approximate and quick analysis. This method has been applied only for vertical loading conditions.  Substitute frame method  Substitute frame method assumes that the moments in the beams of any floor are influenced by loading on that floor alone. The influence of loading on the lower or upper floors is ignored altogether. The process involves the division of multi-storied structure into smaller frames. These sub frames are known as Equivalent frames or Substitute frames. The substitute frames are formed by the beams at the floor level under consideration, together with the columns above and below with their far ends fixed.  The sub frames are usually analyzed by the moment distribution method, using only Two cycle of dist...