Unit 20: Principle of Structural Design | Calculate the axial load-carrying capacity of steel and reinforced concrete columns

Axial loading concept and overview

Bending moment and axial loads because of ordinary stresses on the cross-section column. We can identify the normal stresses from this load combination in a similar way we can also analyse the ordinary stresses because of bending only in the beam with dual exceptions.

• The normal stress sum is now equivalent to the PU axial load rather than equal to zero.
• We collect the moment regarding the cross-section column centroid, rather than the compressive stress centroid on the concrete.
• We can calculate the internal force acting in that ultimate strength column according to the beam.
• Evaluate a profile of strain for the cross-section column. Finally, the strength of the column shows when the comprehensive skin in the concrete gets 0.003 just according to the beam.
• Evaluate the stresses in the steel and concrete
• Evaluate the resultant stress.
• The stress resultant sum is equal to the Pn axial capacity of the column.
• The accumulation of moment resultant by every resultant stress regarding the centroid of the column is equivalent to the moment potential of the column (Mn)

On the other hand, the beam contains only one capacity of the moment, a column contains what`s the tile moment capacity and axial for every ratio of Pn or Mn. Just ratio is known as the city for the demonstration of the cause.

Reinforced Concrete Column:

The axial capacity plot of Pn and Mn moment capacity is known as the interaction diagram. Every point on the diagram of interaction is connected with a profound profile of strain for the cross-section column. Here is a diagram of interaction that has three significant points every point has a difficult region between these points such as,

Point 1 to point 2 is controlled failures:

The concrete gets crushed before the Steel tension (for this layer from the face of compression) yields. The capacity of moment minimises because Steel could not reach its complete strength.

Point 2 failure of balance:

• A failure of the balance occurs at the time of concrete.
• Crushes of 0.003 in a similar tension yield steel equivalent to 0.002.

Point 2 to point 3 failure of tension controlled:

• Section, the area of compression may maximise beyond the area by steel in tension.
• A large force of compression leads to greater moments.

Point 3:

Here column is considered a beam. This area of compression is limited and balanced by steel tension.

The Factor of Strength Reduction:

The minimised axial capacity of the nominal and minimised capacity of the nominal moment is attained from the strength calculation factors that emphasise the strain in steel tension.

Maximum Steel Capacity:

The limits of ACI in axial force in a column between section 10.3.6 to 0.85 Pn, maximum = Φ Pn, max = Φ fc Ag – As (flat portion on the edge of ΦMn, ΦPn curve) divers methods exist to check the normal mix stress because of axial nominal and column. Here are two methods discussed:

1. Single point- useful at the time of checking columns for just loads in one set.
2. Multipoint (complete diagram of interaction) useful at the time of checking column for versatile loads with the set.

Long Foundation Columns:

A column of log slender is falling with the elastic buckling at the time of an axial comprehension load arrives at a complex value. Leonard Euler who was a Swiss mathematician initially formulated the critical load buckling expression in a column.

He made the critical load buckling expression by giving a useful formula and its assumptions are given below:

1. The loads with comprehension are applicable to drive the critical buckling load formula.
2. The column is accurately straight before applying a load.
3. Every column ends are hinges or frictionless pins that permit the column to buckle through the cross-section axis.
4. The column is prepared of isotropic and homogeneous material.
5. The self-weight column is avoided.

The load of critical buckling Pcr for an appropriate ended column of the pin are given by:

1. E= The elasticity material modules (MPa)
2. I= The least inertia movement of the cross-section (mm4)
3. L=The column length from end to end pin (mm)
4. Constant pi (= 3.1416)

The formula demonstrated above applies to the long column with both pin ends. Moreover, the way to determine the buckling load for a long column with other conditions of the supports is known as the effective column height or affected length.

Corrosion of Steel Reinforcement in Concrete:

Steel corrosion in concrete is a process of electrochemistry in which the electrochemical utilises its potential to generate corrosion which can be generated in two methods:

Cells composition can be generated when two different metals are connected in concrete such as aluminium conduit pipes and steel rubbers. When important variations exist in the characteristics of the Steel surface.

Concentration cells can be generated because of differences in the dissolved concentration ions near Steel such as chloride, Oxygen and alkalies.

The electrochemical potential differences may arise from the differences in the concrete environment. The cells of electrochemistry also generate because of the variation in the salt concentration in the cell. Therefore, due to different oxygen access.

Therefore, one of the two metals or some of the metal particles where only one metal is present becomes anodic and the other is cathodic. The fundamental changes of the chemical occur in the cathodic and anodic areas.

Reaction on anode:

Fe- > Fe
Fe++ +2(OH)- -> Fe(OH)2 (ferrous hydroxide)
4Fe(OH)2 +2H2O + O2 -> 4Fe(OH)3 (ferric hydroxide)
(water) (air) 2Fe(OH)3 ->Fe2 × O3 × H2O + 2H2O --- Hydrated ferric oxide (rust)

Reaction on cathode:

4e- +O2 + 2H2O ->4(OH)-