Concept:

The Bending equation:

$\frac{M}{I}=\frac{E}{R}=\frac{\sigma }{y}$

Where M= bending moment, I= moment of inertia, E= modulus of elasticity, Ris radius of curvature, $\sigma$ = bending stress, y is distance of neutral axis.

Calculation:

Given: b = 60 mm, d=150mm, l=4 m, y = d/2 = 75 mm

Bending moment is

 $M=\frac{wl}{4}$

$M=\frac{10\times 4}{4}$

M = 10 kNm

The moment of inertia is 

 $I=\frac{b{d}^3}{12}$ = $\frac{60\times {150}^3}{12}$ =16875000 mm⁴ 

The maximum bending stress induced in beam section

$\frac{M}{I}=\frac{E}{R}=\frac{\sigma }{y}$

${\sigma }_{max}=\frac{M}{I}\times y$

${\sigma }_{max}=\frac{10\times {10}^6}{16875000}\times 75=44.44MPa$

Concept:

As per bending formula:

$\frac{\sigma }{y}=\frac{M}{I}=\frac{E}{R}$   

Where

M = bending moment due to load, σ = bending stress, E = Modulus of Elasticity, R = radius of Curvature, y = distance of outer fibre from neutral axis

I is MOI about a neutral axis and it is given as:

$I=\frac{b{d}^3}{12}$

Calculation:

Given:

E = 2 × 10⁵ N/mm², R = 10 m = 10 × 10³ mm, A = 120 mm × 20 mm, y = 10 mm

As we know,

$\frac{\sigma }{y}=\frac{E}{R}$

$\frac{\sigma }{10}=\frac{2\times {10}^5}{10\times {10}^3}\Rightarrow \sigma =200N/m{m}^2$

A body said to be in motion when it changes its position with respect to or bodies. The relative change in position is called motion. The motion involves both space and time.

In T beams, maximum bending moment is less because of sagging moment is effectively resisted. The maximum deflections are also less in se beams. They are preferred for larger spans when compared to simply supported beams.

The most common type of Stairs arranged with two adjacent flights running parallel with mid landing. Where space is less, dog legged staircase is generally provided resulting in economical utilisation of available place.

Stairs provide access for various floors in a building. The stairs comprises series of steps with landings at appropriate intervals. The stretch between two landings may be termed as a flight.

The column dimensions shall be such that it fails by material failure only (crushing due to compression) and not by buckling. To avoid failure of column buckling clause 25.3 of IS 456 recommends slenderness limits for column.

Ductility is property of a material by which material can be drawn into thin wires after undergoing a considerable deformation without rupture. The mild steel, silver, tor steel, aluminium etc. are considered as examples for ductility.

Concept:

Shear stress at Junction of flange and web is given by,

τ = $\frac{FAY?}{Ib}$  

where,

F = Force applied

A = Area of flange, I = Moment of Inertia of I section, be t= width of web.

Y? = Distance of centroid of flange from N.A.

Calculation:

Let shear stress at flange at junction of flange and web = τ₁ 

width of flange, b₁ = 100 mm

width of web, b₂ = 20 mm 

Let shear stress at web at junction of flange and web = τ₂ 

Then,

τ₁ = $\frac{FAY?}{I{b}_1}$  ------- 1

τ₂ = $\frac{FAY?}{I{b}_2}$  --------2

$\frac{{\tau }_1}{{\tau }_2}=\frac{b_2}{b_1}$

$\frac{{\tau }_1}{{\tau }_2}=\frac{20}{100}$

τ₂ = 5 τ₁ 

RCC work maybe in foundations, columns, lintels, beams, floor& slabs estimate is prepared in cubic metres. In absence of detailed design, percentage of steel reinforcement is taken for lentils 0.7 to 1% and foundation raft footing it is 0.5 to 0.8%.