INTRODUCTION TO STRUCTURAL ANALYSIS...PART ONE

-



Everyday construction activities are done for erection of different structures, the erected structures should be designed so they can be safe and serviceable for desired lifetime.

One of the important stages in designing structures so that they can be safe and serviceable is structural analysis.

Structural analysis is an integral part of structural design which deals with determining the stresses and resistance of structure to the loading.

In analysis loads or stresses can be classified as external loads and internal loads, where by external loads(stresses) comprises of applied loads and reactions while internal  loads comprises of resultant forces, axial forces, shear forces and bending moment.

Reactions and supports

Support is any structural member that is provided to carry or provide support to a loading.

Reactions are what the support offer as resistance when subjects to loading, so these are forces offered by supports to restrain the structure.



Reactions are always acting perpendicular (normal) to the support or supporting surface or plane.

There are three types of support that are normally seen or observed in structural analysis which are fixed support, pin support and  roller support.

Fixed support is the kind of support that has no translation or rotation in any direction; this means fixed support does not both allow movement of a structure and rotation about a point in any direction.



So, the fixed support offers three resistances (reactions) two in translation (vertically and horizontally restrained) and in rotation of a structure (moment is restrained).

Pin support is the kind of support that has no translation in any direction but has rotation about a point, this means pin support does not allow movement of structure in any direction but allow rotation about a point. Below are the symbols of pin supports.




So, the pin support offers two reactions in translation (vertically and horizontally restrained) and moment is not restrained.

Roller support is the kind of support that has translation in one direction and rotation in any direction, this means this support allow movement in one direction (either vertically or horizontally restrained) and moment is not restrained. 



 


STABILITY OF THE STRUCTURE

In structural analysis the structures can be classified as stable and unstable structures on basis of structural stability, stable structures are further classified as determinate and indeterminate structure.

So in structural analysis we have determinate structures, indeterminate and unstable structures.

Determinate structures

These are structures which provide resistance to both effect that could result from loads without extra resistance or support left, these structures are stable structures where by its stability depends on both supports, failure of one support make it unstable.

The stability of the structure is the composite of stability of its structural members, so determinate structural members make the whole structure determinate.

Indeterminate structures 

These are structures which provide resistance to both effect that could result from loads with extra resistances or supports left, these structures are stable structures where by its stability does not depends on both supports, failure of one support does not make it unstable.

The stability of the structure is the composite of stability of its structural members, so indeterminate structural members make the whole structure indeterminate.

Unstable structures

These are structures which do not provide resistance to both effects that could result from loads, these structures are unstable as they allow either translation or rotation or both.

The stability of the structure is the composite of stability of its structural members, so unstable structural members make the whole structure unstable.

HOW TO CHECK STABILITY OF STRUCTURE

Stability of the structure is checked by determining the degree of indeterminacy (n) of structure and then checks if it is determinate, indeterminate or unstable structure.

 For determinate structure the degree of indeterminacy is "0", for indeterminacy structure degree of indeterminacy is "greater than 0" and for unstable structure the degree of indeterminacy is "less than 0".

For n = 0 (Statically determinate structure)

       n > 0 (Statically indeterminate Structure)

       n < 0 (Unstable structure)

 

 

Case 1. For a beam

From n = r-3 where n - Is degree of indeterminacy

                                r - Is the number of reaction in the system.

Case 2. For a beam with internal support

From   n = r-(3+ec) where n - Is degree of indeterminacy

                                         r - Is the number of reaction in the system.

Internal support can be either internal hinge or internal roller where by ec for internal hinge is 1(ec = 1)  as it lacks one resistance (moment restraint) and ec for  internal roller is 2 (ec = 2) as lacks two resistances (one translation and moment restraints)

Case 3. For a truss

From    n = r + m – 2j where n - Is degree of indeterminacy

                                               r - Is the number of reactions.

                                               j - Is the number of joints

For a full document click on button below



Comments

Post a Comment

Popular posts from this blog

HOW TO FIND THE MEAN GIRTH OF THE SIMPLE BUILDING

-
Image
Mean girth of building , this is the centerline perimeter or circumference of the building, which describes length of the building. The following text show how to find the mean girth of simple building plan shown below for superstructure walling which can help in quantity determination of different materials to be applied for paint work, plaster work, blocks or brick work. Important Terms 1. External Dimensions.   These are dimensions measured from      external surface of the building's walls, these always show the extent of building on plot. 2. Internal Dimensions. These are dimensions measured from internal surfaces of the building walls, these always show sizes of rooms. 3. Corner. These are interconnection or points where two non colinear walls meet. 4. Recesses. There are the partition or adjoining walls which forms rooms or which were not considered in exterior girth of building determination. Ti...
Read more

HOW TO CALCULATE THE NUMBER OF BLOCKS REQUIRED FOR WALLING

-
Image
The number of blocks required for wall can be calculated from the area of the wall which will be constructed by the block of certain size. The mean girth of the simple obtained as calculated from previous post is 28.85m The common (standard) size of the conc. block is 150 x 230 x 450; the wall length (mean girth) of building is multiplied by the height of the walls to find the total  surface area of wall, for a wall of height 2.8m with the opening as shown in the table below The table below shows windows and doors schedule for doors and windows used   Schedule for windows used PORTIONS WIDTH(m) HEIGHT(m) NUMBER(m) AREA(m 2 ) A 1.50 1.50 3 6.75 B 1.50 1.50 2 4.50 C 0.7 0.7 1 0.49 1.00 1.50 1 1.50 D 1.50 1.50 1 2.25 1.00 1.50 1 1.50 Total Area of All Wind...
Read more

HOW TO CALCULATE AMOUNT OF MORTAR PER S.Q.M FOR BLOCK WALL

-
Image
HOW TO CALCULATE AMOUNT OF  MORTAR  PER S.Q.M FOR BLOCK WALL The amount of cement paste required as mortar per square meter can be calculated through the following steps 1.       Knowing the dimension of the blocks to be used for construction. Here, let’s say we use the cement concrete block of size 150 x230 x450 where by 150 s the thickness of the wall. These dimension s (all dimension are in mm) help to find the area of one block forming wall surface as follows Area of one block = 230 x 450                              = 103,500mm 2 2.        Knowing the new dimension of blocks with cement mortar. New dimension of concrete block means the height and length of a block with the thickness of mortar which is 15m, then the new height id 245mm and new length is 265mm Fr...
Read more