Design of Staircase, walls, footings, retaining walls, Miscellaneous Study Notes

Technical terms in Stairs

1. Tread: The horizontal upper portion of a step
2. Riser: It is the vertical distance between two consecutive treads and riser is the vertical portion of step.
3. Winder: The radiating or angular tapering step.
4. Landing: The horizontal slab provided between two flights.
5. Nosing: The outer projecting edge of a tread.
6. Flight: This consists of a series of steps provided between landing.

Classification of Stairs

1. Straight Stairs: This consists of steps leading in the same direction. It is provided in long in long narrow stairs case.
2. Dog-legged Stair: In the type, the succeeding flights rise in opposite directions

1. Effective Span

Clause 33 of IS 456 gives the ruler for calculating the effective spans.

a. When the stairs span longitudinally and are supported at the top and bottom by beams, the effective span is the distance between the respective centres of beam.

1. When the stairs span longitudinally with the landing slab also spanning in the same direction as the stairs, the effective span is the centre to centre distance between the supporting beam or walls. 

1. When the stairs span longitudinally and are supported by landing an top and bottom, which span in transverse direction, the effective span is the total going of the stair plus the half width of the landing on each end or 1m whichever is smaller. 

4. In the case of stair spanning transversely (horizontally in the transverse direction) the effective width of stair is taken as effective span. 

 Loads on Stair Slabs

The dead load to be considered on the stairs includes-

(a)   self wt. of the stair slab

(b)  self wt. of step slab-type stairs, [it is taken as 25 kN/m³ × Average thickness of step].

(c)   self wt. of finish

RETAINING WALLS

INTRODUCTION

Retaining walls are usually built to hold back soil mass. However, retaining walls can also be constructed for aesthetic landscaping purposes.

CLASSIFICATION OF RETAINING WALLS

EARTH PRESSURE (P)

• Earth pressure is the pressure exerted by the retaining material on the retaining wall. This pressure tends to deflect the wall outward.
• Types of earth pressure :
• Active earth pressure or earth pressure (P_a) and
• Passive earth pressure (P_p).
• Active earth pressure tends to deflect the wall away from the backfill and opposite for passive earth pressure.

ANALYSIS FOR DRY BACK FILLS

Maximum pressure at any height, p = k_aγh

Total pressure at any height from top,

p_a = 1/2[k_aγh]h = [k_aγh²]/2

Bending moment at any height

M = p_axh/3 = [k_aγh³]/6

∴ Total pressure, P_a = [k_aγH²]/2

∴ Total Bending moment at bottom,

M = [k_aγH³]/6

Where, k_a = Coefficient of active earth pressure

 = (1 – sinϕ)/(1 + sinϕ) = tan²ϕ

 = 1/k_p, coefficient of passive earth pressure

• ϕ = Angle of internal friction or angle of repose
• γ = Unit weigh or density of backfill

BACKFILL WITH SLOPING SURFACE

p_a = k_a γH at the bottom and is parallel to inclined surface of backfill

• 
• Where θ = Angle of surcharge

∴ Total pressure at bottom

= P_a = k_a γH²/2

DESIGN OF MASONRY STRUCTURES

Masonry in general is defined as any structural assemblage of masonry units like stones, bricks, blocks etc. with a binding material which is known as mortar. The walls of the masonry building and the building itself are designed to be stable, strong and durable enough to withstand the most severe combination of loads called as design load. Masonry in general is defined as any structural assemblage of masonry units like stones, bricks, blocks etc. with a binding material which is known as mortar. The walls of the masonry building and the building itself are designed to be stable, strong and durable enough to withstand the most severe combination of loads called as design load.

TERMINOLOGIES

• Bed Block: A block bedded on a wall, a column or a pier in order to disperse a concentrated load on a masonry element.
• Cavity wall: It is the wall consisting of two leaves with each leaf separated by a cavity and ties together with metal ties or the bonding units in order to ensure that the two leaves act as one unit. The space between the two leaves is either left free as a continuous cavity or filled with non-load bearing insulating or water proofing material.
• Curtain wall: It is a non load bearing wall subjected to lateral loads only. It may be laterally supported by vertical or horizontal structural members.
• Effective height: It is the height of wall or column which is required for computing the slenderness ratio.
• Grout: It the mixture of cement (or any other binding material). sand and water with a pourable consistency for filling the voids.
• Leaf: Inner or outer section of a cavity wall is called as leaf.

Maximum slenderness ratio for reinforced load bearing wall

 MASONRY REINFORCEMENT

Table: Reinforcement specification in load bearing construction

DESIGN LOADS

Load Combinations

In structural design of masonry structures, the most commonly adopted design philosophy is the allowable stress design method. As per this design method, the structure shall be designed for the following load combinations:

1. DL + IL
2. OL + IL + WL (or EQL)
3. DL + WL
4. 0.9DL + EQL

DL: Dead Load, IL: Imposed Load, WL: Wind Load, EQL: Earthquake Load

Permissible Loads and Stresses

In the design load combination wherein wind load (or earthquake load) is being considered, there the permissible stresses may be increased by 33.33%.

Alternatively, instead of increasing the permissible stresses, we can use 25% reduced load for load combinations which involves Wind load (or earthquake load) and take into account the full permissible stresses. Thus the modified design load combinations for loads involving wind load (or earthquake load) are:

1. 0.75 (DL + IL + WL (or EQL))
2. 0.75 (DL + WL)
3. 0.75 (0.9DL + EQL)

EFFECTIVE HEIGHT OF WALLS

It is the height of waif or column which is required for computing the slenderness ratio.

Table: Effective height of wall

Footing/Foundation

INTRODUCTION

Foundation is important part of any superstructure. It transfers load from superstructure to soil.

Bearing capacity of soil

Bearing capacity of soil governs the dimensions and depth of foundation. Under no case the loading on foundation can be greater than bearing capacity of foundation

(A) Gross Bearing capacity:  Total bearing capacity at based on foundation which includes weight of foundation, Online Classroom Program structure load, earth lying over footing.

(B) Net Bearing capacity: It can be defined as follows

Net bearing capacity= Gross Bearing capacity - W

W= weight of soil at level of footing before trench was made for footing

Depth of foundation

 following formula must be use to find the depth of foundation

Types of Foundation

Based on depth it can be into two parts

(i) Shallow foundation- if total depth (D) of footing is less than width (B) of foundation then foundation is called shallow foundation.

(ii) Deep foundation- If total depth (D) is less than width (B) of foundation than foundation is called deep foundation.

Nominal cover as per IS 456:200

Minimum Nominal cover as per exposure condition

DESIGN OF FOOTING

Let’s take an example to understand important aspect of footing

Example: Design a square footing using LSM for a column load of 1000 kN. If bearing capacity, density of soil is 150 KN/m² and 20 kN/m³. Use M30 /Fe 415.

Dimension of column= 500 ×500 mm

Sol.

Axial load P₁ = 1000 kN

Weight of footing P₂ = 0.20 × P₁ = 200 kN

Note = P₂ can be assumed to 10 to 20% of

Total load = P_T = 1200 kN

(i) Area of footing required

Area = P_T/q₀

q₀ = bearing capacity of soil

Area =  = 8 m²

Assume 4 m × 4 m square footing is provided

Area provided = 16 m² > Area required

(ii) Net soil pressure

w₀ =P₁ /A= 62.5 kN/m²

For LSM design w₄₀ = 1.5 × w₀ = 93.75 kN/m²

1.5 → Partial factor of safety

(iii) Check for bending moment

As per our design

a = b = 500 mm

L = B = 4 m

{In case of rectangular footing a, b, L, B}

will not be same

for 1 m width → about xx

= 143.55 kNm

Moment about y-y

For 1 m width

In case M_ux and M_uy comes differently then take maximum value

(iv) depth of footing 

(v) Check for shear

Critical section for one way shear is at Q from face of column

τ_c = permissible shear stress

τ_c = 0.29 → for M30

V_u = 93.75 × 10³ × 1×[(4-0.5)/2-0.3]=

= 13594 kN

For B = 1m

τ_V =V_u/Bd  = 0.54

τ_V > τ_c → Not safe in shear increasing depth (G) of footing to 600 mm

V_u = 93.75 × 10³ × 1×[(4-0.5)/2-0.6]=

= 107.81 kN

τ_V = 0.17 < τ_c → safe

now so new depth of footing = 600 mm

overall depth of footing = 660 mm

(vi) Check for punching shear / two way shear

Note →

Critical section for punching shear is at d/2 for five of column all-around

P_net = P_u – W_u (a + d) (b + d)   

P_net = 1.5 × P – W_u (a + d) (b + d)

d = 0.6

k_s = 0.5 + β_c

= 0.5 + (b/a)

= 0.5 + 1 = 1.5  

maximum possible value of k_s =1 so

k_s = 1

τ_cp = 1.36 N/mm² > τ_vp → safe

so d = 600 mm

D = 660 mm

(v) Area of steel

(3) Total area of steel

= L × A_st = 4 × 560 = 2240 mm²

Total no of  bars for 16 mm ϕ

n= 2240/[(π/4)×16²]=12

 (4) number of central bend

∴  for width all value remains same

(5) check for bearing

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