Test: Theory of RCC- 1 - Civil Engineering (CE) MCQ

Effective span
A. Simply supported beams and slabs (l_eff)

Here, l_o = clear span = distance between the inside surfaces of the span supports for beam (see figure below)
w = width of the support
d = depth of beam or slab
B. For continuous beam
i) If the width of support <1/12 of clear span

ii) If the width of support >1/12 of clear span
a) When one end fixed other end continuous or both end continuous.

I_eff = I₀
b) When one end continuous and another end simply supported.

C. Cantilever
i)


ii)


The effective span for a cantilever slab at the end of a continuous slab is equal to the length up to the centre of the support or the length up to face of support plus half of the effective width.

Development Length:
A development length is the amount of rebar length that is needed to be embedded or projected into concrete to create desired bond strength between the two materials and also to develop required stress in steel at that section.
As per IS 456: 2000, clause 26.2.1,
The development length is given by: 
L_d = φσ_s/4τbd
where
ϕ = nominal diameter of the bar
σ_s = stress in the bar at the section considered at design load
τ_bd = design bond stress
Points to be remembered:
(1) The development length includes anchorage values of hooks in tension reinforcement.
(2) For bars other than circular cross-section, the development length should be sufficient to develop the stress in the bar by the bond.

Reinforced Concrete Structures Question 5 Detailed Solution
Concept:
When a cantilever beam is loaded vertically downward, then all the fibers above the neutral axis got elongated and all the fibers below the neutral axis got contracted due to which tensile stress is induced in all fibers above the neutral axis and compressive stress is induced in all fibers below the neutral axis.
Therefore, the maximum compressive stress will be at the bottom fiber, because that fiber has minimum section modulus.

Concept:
Creep is the plastic permanent deformation of a structure under constant load for a very long period of time.
It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material. Creep is more severe in materials that are subjected to heat for long periods and generally increases as they near their melting point.
It occurs due to dead load only.
Factors affecting creep
1. Type of loading
2. Magnitude of load
3. Time
4. Temperature
If temperature is more, creep is more and if the temperature reaches to half of melting point temperature the creep is intolerable. Such a temperature is defined as homologous temperature. 

Explanation:

• A minimum area of tension steel is required in flexural members (like beams) in order to resist the effect of loads and also control the cracking in concrete due to shrinkage and temperature variations.
• Minimum flexural steel reinforcement in beams: CI. 26.5.1.1 of IS 456:2000 specify the minimum area of reinforcing steel as:

= 0.34% for Fe 250
= 0.205% for Fe 415
= 0.17% for Fe 500
For flanged beams, replace 'b' with the width of web 'b_w'
Important Points

• The maximum area of tension steel in beams(Intension beams as well as compression beam) provided as per IS 456:2000 = 4% of gross area
• The minimum area of tension steel in the slab as per CI. 26.5.2 of IS 456:2000
  • A_stmin = 0.15% of gross area for Fe 250
  • A_stmin = 0.12% of gross area for Fe 415

Confusion Points

• Minimum flexural steel reinforcement in the slab is based on shrinkage and temperature consideration and not on strength consideration because, in slabs, there occurs a better distribution of loads effects unlike in beams, where minimum steel requirement is based on strength consideration.

Slender column: Cross sections in which the elements buckle locally even before the attainment of yield stress are called slender sections.
The column is classified based on its slenderness ratio.

Considering the x-axis is as major axis because I_xx is greater and the y-axis as the minor axis a > b ⇒ I_xx > I_yy
Slenderness ratio = Leff/Lateral dimension

So,
λ_max ≤ 3 → Pedestal
3 < λ_max < 12 → short column
12 ≤ λ_max → Long/Slender column

Heterogeneous Material:

• Heterogeneous refers to a structure with dissimilar components or elements, appearing irregular or variegated. So, a heterogeneous material is a mixture of two or more materials.
• Concrete is a heterogeneous (Composite) material consisting of cement water, fine aggregates, and coarse aggregates. These are the ingredients of conventional concrete.
• Cement may be called a homogeneous material but concrete is not.
• Concrete's property is dependent on the individual properties of cement, sand, and coarse aggregates.
• The behavior alters greatly in a different direction due to a number of reasons.
• There are greater uncertainties in getting the same properties in all directions.

Note:

• A material is said to be homogeneous when it is properties are the same in all directions. otherwise, it is a heterogeneous material.

As per IS 456: 2000, ANNEX B
This value of the modular ratio partially takes into account the long-term effects of creep.
σ_cbc for M20 is 7 MPa and the modular ratio comes out to be 13.
The modular ratio is given by
m = 280/3σ_cbc
For M20 concrete
σ_cbc = 7 N/mm²
∴ m = 280/(3x7) = 13.23
Note: It is expected from students to know value of σ_cbc which is nearly 1/3rd of characteristics compressive strength. Please don't report questions for no data or wrong question.

As per IS 875 Part 2, clause 3.1, Imposed Floor load for residential building are: