Statically Determinate and Indeterminate Structures

 ◆Statically Determinate Structures 

•A structure is said to be determinate it condilions of static equilibrium are sufficient to analyse the structure. 

•In determinate structures, bending moment and shear force are independent of properties of material and cross-sectional  area. 

•No stresses are induced due to temperature changes. 

•No stresses are induced due to lack of lit and support settlement.

 ◆Statically Indeterminate Structures 

•A structure is saíd to be statically indeterminate it condilions of static equilibrium are not sufficient to analyse the structure. 

•To analyse these structures, additional compatibility condilions are required. 

•In indeterminate structures, bending moment and shear force depends upon the properties of material and cross-sectional area. 

•Stresses aro induced due fo temperature variations. 

•Stresses are induced due fo lack of lit and support settlement.

Degree of Indeterminacy 

The degree of indeterminacy can be divided into: 

1. Static indeterminacy, which can bo classified as 

(a) external indeterminacy 

(b) internal indelerminacy 

2. Kinematic indeterminacy

Static indeterminacy

1. External Static Indeterminacy

It is the total number of additional equations required to determine the external forces.

In general Degree of external static indeterminacy,

Dse = r - e

where r = Number of unknown reaction components

e = Total number of equilibrium equations

For different types of structure it is given as,

(i) Plane frame or 2D frame Dse = r – 3 

(ii) Space frame or 3D frame Dse = r - 6

2. Internal Static Indeterminacy: -

It is the total number of additional equations required to determine the internal forces.

For different type of structure it is given as

(i) Pin jointed plane frame, Dsi = m – (2j -3) 

(ii) Pin jointed space frame, Dsi = m – (3j -6) 

(iii) Rigid jointed plane frame, Dsi = 3C – r’

(iv) Rigid jointed space frame, Dsi = 6C – r’

Where, m = total number of members

j = total number of joints

C = total number of cuts required for open configuration

r’ = Number of additional equation due to hybrid joints.

Total degree of static indeterminacy is the sum of internal and external static indeterminacy.

Ds = Dse + Dsi

(i) Pin jointed plane frame, Ds = m + r – 2j

(ii) Pin jointed space frame, Ds = m + r – 3j

(iii) Rigid jointed plane frame,Ds = (r - 3) + (3C – r’) OR 3m + r – 3j

(iv) Rigid jointed space frame,Ds = (r – 6) + (6C – r‘) OR 6m + r - 6j

Where, 

m = number of members

j = number of joints

r’ = number of additional equations due to hybrid joints

r = number of external reactions

Kinematic indeterminacy

Kinematic indeterminacy also known as degree of freedom (DOF) is the 

total number of independent joint displacement. A joint can have two 

types of displacements in general; rotation and linear displacement. 

Dk = aj – r + r'

(1) Pin jointed plane frame, Dk = 2j - r

(2) Pin jointed space frame, Dk = 3j - r

(3) Rigid jointed plane frame, Dk = 3j – (r + m) + r’ 

(4) Rigid jointed space frame, Dk = 6j – (r + m) + r’ 

Where, a = DOF 

j = Number of joints

m = Number of members

r = number of reactions

r’ = number of additional equations due to hybrid joints

FRICTIONS

 1. INTRODUCTION :: 

(i) When two surfaces in contact have relative motion or have tendency of motion with each other then a force acts at the point of contact of the object and this force is called frictional force. 

(ii) The force of friction is always in a direction opposite to which the body tends to move 

(iii) It is paralel to the surface 

(iv) Frictional force is independent of the area of surface in contact 

(v) The force of friction depends on the nature of material of the surface in contact. 

(vi) Friction is a non-conservative force i.e. work done against friction is path dependent. 

(vii) Generally many of us have a misconception that friction opposes the motion of a moving body but it favours the motion of a body. It opposes the relative motion between the two bodies. When a person walks forward, he pushes the ground backward. The rough surface of ground exerts a forward force which causes the motion of the person.

2. TYPES OF FRICTION 

Friction is of two types 

(a) Static friction (b) Kinetic friction 

Now let us have some discussion on these types of friction 

2.1 Static friction : 

(i) Frictional force between two surfaces when there is no relative motion between them is called static friction. 

(ii) Static friction is self adjusting in nature. It adjusts its magnitude in such a way that together with other forces applied on a body, it maintains relative rest between two surfaces. 

(iii) The value of static friction lies between 0 and μₛN i.e 0 ≤ fₛ ≤ μₛN where μₛ is coefficient of static friction and N is normal force 

(iv) There is no energy loss due to static friction. We may perform work against static friction or static friction may perform work. 

2.2 Kinetic friction : 

(i) Frictional force between the two surfaces which are in relative motion is called kinetic friction. 

(ii) The magnitude of the kinetic friction is proportional to the normal force acting between the two surfaces i.e. fₖ ∝ N   fₖ = μₖN  where μₖ is coefficient of kinetic friction. 

(iii) This force of kinetic friction always. acts opposite to the direction of motion. 

(v) Work done against kinetic friction is nonconserved i.e. converted into heat. So in case of kinetic friction, there is always an energy loss

NOTE : If nothing is specified for μₖ and μₛ then we assume that both are equal. Theoretically

μₖ < μₛ

BUILDING, CONSTRUCTION & MATERIAL

•  Gypsum is a mechanically formed sedimentary rock.
•  Quartzite is a silicious rock.
•  Slate is formed by metamorphic action on shale.
•  Heavy stone is suitable for retaining wall.
•  Hard stone is suitable for rubble masonry.
•  Soft stones is suitable for ornamental work.
•  Quartzite has most weather resisting characteristics.
•  A good building stone should not absorb water more than 5%.
•  Compact sand stone has more fire resisting characteristics.
•  Weight test is conducted on a stone used in docks and harbours.
•  Granite stone is best suited for construction of piers and abutments.
•  Crushing strength of good building stone should be more than 100mpa.
•  Specific gravity of most of the building stone lies between 2.5 to 3.
•  Pith-annular rings-heartwood-sapwood-cambium layer-inner and outer bark.
•  Shisham is hard wood and offer maximum resistance to the white ants.
•  Star shakes-the radial splits which are wider on the outside of the log and narrow towards the pith.
•  Chir and deodar yields soft wood.
•  Mulberry tree used for making of sports goods.
•  Dry rot caused due to lack of ventilation.
•  Foxiness caused due to over maturity.
•  Honey combing caused due to-seasoning.
•  Strength of the timber is maximum in the parallel direction.
•  10% to 12% is the moisture content of well seasoned timber.
•  The age of the tree can be known by annular rings.
•  1st class timber has an average life of more than 10 years.
•  1st class brick should not absorb water more than 20% when immersed in water for about 24 hours, 22% for 2nd class bricks and 25% for 3rd class bricks.
•  Crushing strength of 1st class bricks not less than 10.5N/mm^2, 7.5N/mm^2 for 2nd class bricks.
•  The main function of alumina in brick earth is to impart plasticity.
•  The percentage of alumina in good brick earth is 20 to 30%.
•  Excess of alumina in brick earth cause crack and warp on drying.
•  Excess of silica cause brittleness.
•  20*10*10 cm is the nominal size of the brick.
•  19*9*9cm is the standard size of brick.
•  50 to 60 % silica in good brick earth.
•  Silica makes the brick to retain the shape.
•  Kneading –the process of mixing the clay water and other ingredients called.
•  60 to 70% turn over in clamp burning where as 80 to 90% turn over in kiln burning.
•  Pug mill used for preparation of clay.
•  Refractory bricks used in combustion chambers.
•  The frog of the brick generally kept on the top face of masonry.
•  500 bricks required for one cubic metre of brick masonry.
•  Quick lime is calcium oxide.
•  Hydraulic lime is obtained from burning of kankar.
•  Lime and silica are the main ingredients of the Portland cement.
•  C3A is responsible for all undesirable properties of cement.
•  Le chate lier apparatus is used for testing the soundness of cement.
•  Vicat apparatus used for testing setting time of cement.
•  C3A is responsible for intial setting time of cement.
•  The intial setting time for ordinary Portland cement not less than 30minute.
•  The final setting time should be 10 hour.
•  The normal consistency of ordinary Portland cement is 30%.
•  Early attainment of strength of cement in rapid hardening of cement is due to finer grinding.
•  After storage the strength of the cement is decreases.
•  Addition of pozzolana to ordinary Portland 
• cement cause shrinkage.
•  Gypsum consists of caso4 and H2O.
•  25mm to 50mm is the slump recommended for mass concrete.
•  Low heat cement is used in massive concrete structures.
•  Calcium chloride is the common admixture to accelerate the intial setting time.
•  The basic purpose of retarder in concrete is to increase the intial setting time of concrete.
•  Gypsum is most commonly used retarder.
•  Carbon influences the maximum properties in steel.
•  Wrought iron is the purest form of iron.
•  The ultimate tensile strength of steel is 420N/mm^2.
•  0.25% of carbon in mild steel.
•  Yield stress is used for identifying the quality of structural steel.
•  Flemish bond –alternate courses of header and stretcher.
•  English bond-alternate header and stretcher.
•  The pressure acting on the stones in stone masonry should be perpendicular to the direction of bedding planes.
•  Queen closer-the brick is cut into 2 equal parts in length wise.
•  English bond is provided in masonry for carrying heavy loads.
•  Slenderness ratio-effective length to least radius of gyration, for masonry walls not more than 20.
•  The differential settlement in case of sandy soil not more than 25mm.
•  In case of foundation on black cotton soil the most suitable method is to replace the poor soil.
•  Grillage foundation is the most economical foundation to transmit the heavy load.
•  Batter pile is used to resist the horizontal and vertical forces.
•  0.9m is the minimum depth of the foundation on clay soil.
•  The bearing capacity of a water logged soil can be improved by draining the soil.
•  Depth or height of arch-is the perpendicular distance between the intrados and extrados.
•  Flat roof is constructed where the rainfall is less and temperature is high.
•  Pitched and sloping roofs are suitable for coastal region.
•  The maximum number of steps generally restricted is 12.
•  Sum of tread and rise must between 400 to 450mm.
•  Minimum width of landing should be equal to width of stairs.
•  In any good stair case the maximum and minimum pitch is 40’ and 25’.
•  Doglegged stairs are half turn stairs.
•  Horizontal projection at head and sill called horns.
•  Revolving door is suitable for entrance in an air conditioned building.
•  Attrition test determines the rate of wear of stones.
•  Efflorescence-formation of white patches on the brick surface due to presence of alkalies.
•  Vanadium steel used in the manufacture of axles and springs.
•  Neoprene is suitable for bearing of bridges.
•  To produce low heat cement it is necessary to reduce the C3A.
•  Timber can be made more fire resistant by sir abel’s process.
•  Creosote is derived from wood or coal.
•  Excess of sulphur in steel results in red shortness.
•  Distemper is used to coat interior surface not exposed to weather.
•  Putty is made up of powdered chalk and raw linseed oil.
•  The limit of proportionality is applied more in the case of mild steel.
•  The compacting factor test determines the workability.
•  The split tensile strength is 10% to 15%.
•  The approximate ratio between the strength of cement concrete 7 to that of 28 days is 2/3.
•  The moisture content of timber is 12%.
•  0.85P times amount of water is used ofr intial setting time, 0.72P for soundness cement.
•  Lime mortar is generally made with hydraulic lime.
•  The texture of sand stone is granular crystalline.
•  Seasoning of timber is required to remove sap from timber.
•  The ratio of youngs modulus of high tensile steel to that of mild steel is about 1.
•  Poly vinyl chloride is thermoplastic material.
•  King closer is related to brick masonry.
•  High alumina cement is produced by limestone and bauxite.
•  The optimum number of revolutions required for concrete mix is 20.
•  Manganese steel used in the manufacture of rails.
•  Gauged mortar is obtained by adding sand and lime.
•  1300’to 1500’ is the temperature range of cement in kiln.
•  Before testing setting time of cement one should be test for consistency.
•  The super plasticizer in a cement paste is disperse the particles, remove air bubbles and to retard setting.
•  Surkhi is added to lime mortar to impart hydraulicity.
•  Increase in fineness of cement results in increase in development of strength and leads to higher shrinkage.
•  The purpose of frog is to form key joint between brick and mortar.
•  Bricks are burnt at a temperature of 900-1200 degree Celsius.

Correction of Chain & Tape

●Corrections Chain

• Correction for standardization • Correction for slope ●Corrections Tape • Correction for standardization • Correction for slope • Correction for Pull • Correction for Sag • Correction for Temperature • Correction for MSL • Correction for misalignment.

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