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CSE - Civil Engineering Study

Table of Contents

Euler's formula for long column- Strength of Material

Euler’s theory: This theory is valid only for long columns only. This theory is valid only when slenderness ratio is greater or equal to cri...

Euler’s theory:

  • This theory is valid only for long columns only.
  • This theory is valid only when slenderness ratio is greater or equal to critical slenderness ratio.
  • For any slenderness ratio above critical slenderness ratio, column fails by buckling and for any value of slenderness ratio less than this value, the column fails in crushing not in buckling.

Euler’s critical load formula is,

`e = (pi^2*EI)/l^2`

  • Euler’s formula is applicable when, Crushing stress ≥ Buckling stress


For mild steel,

E = 2 × 105 N/mm2

σcr = 330 N/mm2

 λ ≥ 80 N/mm2

  • When slenderness ratio for mild steel column is less than 80, the Euler’s theory is not applicable.



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Theories of failure - Strength of Material

Theories of Failure and shapes - Strength Of Material Maximum Principal Stress theory or Rankine theory Maximum Principal stress theory or r...

Theories of Failure and shapes - Strength Of Material


Maximum Principal Stress theory or Rankine theory

Maximum Principal stress theory or rankine theory
Maximum Principal stress theory or rankine theory


Maximum principal strain theory st. venant's theory
Maximum principal strain theory st. venant's theory
st. venant theory or max principal strain theory




Maximum shear stress theory
maximum shear stress theory


maximum strain energy theory
maximum strain energy theory


maximum strain energy theory 




maximum shear strain energy theory
maximum shear strain energy theory 


In short 

For brittle material


Theories of failure


Shape


Maximum Principal Stress theory 

(RANKINE’S THEORY)

Square


Maximum Principal Strain theory 

(St. VENANT’S THEORY)

Rhombus


Total Strain Energy theory 

(HAIGH’S THEORY)

Ellipse


For Ductile material


Theories of failure


Shape


Maximum Shear Stress Theory 

(GUEST AND TRESCA’S THEORY)

Hexagon


Maximum Distortion Energy Theory 

(VON MISES AND HENCKY’S THEORY)

Ellipse






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Contra flexure, Shear Center and Max Shear Stress - Strength of Material

Contra flexure Point occur at Bending Beam - SOM Where Bending Moment changes sign on Bending Moment Diagram. In a bending beam, a point is ...

Contra flexure Point occur at Bending Beam - SOM


  • Where Bending Moment changes sign on Bending Moment Diagram.
  • In a bending beam, a point is known as a point of contra flexure if it's a location at which no bending occurs.
  • In a bending moment diagram, it is the point at which the bending moment curve intersects with the zero lines.
  • In other words where the bending moment changes its sign from negative to positive or vice versa.
  • A point of contra flexure occurs in the overhanging beam.




Important Point

Section

 τmax/τavg 

 τNeutral axis / τavg 

Rectangular/square

3/2

3/2

Solid circular

4/3

4/3

Triangle

3/2

4/3

Diamond

9/8

1




Shear centre: 

  • The shear centre is the point through which if the resultant shear force acts then member is subjected to simple bending without twisting.

Location of shear centre:

  • (i) Shear centre generally does not coincide with the centroid of section except in special cases when the area is symmetrical bout both axis.
  • (ii) Shear centre always lies on the axis of symmetry if exists.
  • (iii) If there are two or more than two axis of symmetry exist, then shear center will coincide with point of intersection of axis of symmetry. In this case shear centre of area will be same as centroid of area.
  • (iv) If a section is made of two narrow rectangles then shear centre lies on the junction of both rectangles.




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Permissible Limit of Solids in water for Concrete - IS 456:2000 - Vk Study Civil

Permissible Limit of Solids in Concrete - IS 456:200 - Vk Study Civil According to Indian Standard Code of Practice 456:2000 Fourth Revision...

Permissible Limit of Solids in Concrete - IS 456:200 - Vk Study Civil

According to Indian Standard Code of Practice 456:2000 Fourth Revision

Permissible limits for solids is shown in table below - Potable water is considered satisfactory for mixing Concrete 


Table 1. Clause5.4 

Permissible Limit for Solids in Water for Concrete

SolidsTested as perPermissible limit,Max
Organic IS 3025
part 18		200 mg/l
InorganicIS 3025
part 18 		3000 mg/l
Sulphates
as SO2 		IS 3025
part 24		400 mg/l
Chlorides IS 3025
part 32		2000 mg/l
for Plain Concrete
ChloridesIS 3025
part 32		500 mg/l
for Reinforced concrete
Suspended
 Matter 		IS 3025
part 17		2000 mg/l





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