Question

Provide a discussion on each of the following topics. When necessary, define the term, explain the term, discuss the purpose and use, and provide sample calculations.

[1] Live load and its variation with tributary area [Tributary Reduction Factor] for a column in a multi-story building.

[2] Design Principles for Structures, and the philosophies behind “Limit States Design”.

Answer 1

1) LIVE LOADS :- The live loads used for the structural design of floors, roof  and the supporting members shall be the greatest applied loads arising from the intended use or occupancy of the building, or from the stacking of materials and the use of equipment and propping during construction, but shall not be less than the minimum design live loads set out by the provisions of this section.

Variations with tributary reduction factor :-

The Live Load Reduction Factor form has the following areas:

• Live Load Reduction Method options. Choose the formula or method, if any, to be used for live load reduction:
• • No Live Load Reduction option. When this option is selected, no live load reduction is performed even if static load cases have been defined as reducible live load type load cases.
  • Tributary Area (Based on Design Code) option.

ASCE7-95 option. When this option is selected, the influence area live load reduction method based on Section 4.8.1 of the ASCE 7-95 Standard is used. The basic formula is as follows:

where,

RLLF =Reduced live load factor for an element

A1 =Influence area of the element

The RLLF factor is limited to Minimum Factor values

ASCE7-05 option - When this option is selected, the influence area live load reduction method based on Section 4.8.1 of the ASCE 7-05 Standard is used. The basic formula is as follows:

The RLLF factor is limited to Minimum Factor values.

ASCE7-10 option - When this option is selected, the influence area live load reduction method based on Section 4.7.21 of the ASCE 7-10 Standard is used. The basic formula is as follows:

The RLLF factor is limited to Minimum Factor values.

AS/NZS 1170.1-2002 option - When this option is selected, the live load reduction method based on Section 3.4.2 of the AS/NZS 1170.1:2002 Standard is used. The basic formula is as follows:

The RLLF factor is limited to Minimum Factor values.

Chinese GB 50009-2001 option When this option is selected, the live load reduction method based on Section 4.1.2 of the Chinese GB 50009-2001 Standard is used. The basic formula is as follows:

The total stories beyond the design element	LLRF
1	1.0
2 to 3	0.85
4 to 5	0.70
6 to 8	0.65
9 to 20	0.60
Over 20	0.55

The RLLF factor is limited to Minimum Factor values -

Eurocode 1991:2002 option -When this option is selected, the influence area live load reduction method based on Section 6.3.1.2(11) of the Eurocode 1991:2002 Standard is used. The basic formula is as follows:

where,

n	=	Number of stories (> 2) above the loaded structural element
	=	0.7 in accordance with EN 1990, Annex A1, Table A1.1.

The RLLF factor is limited to Minimum Factor values (see bullet below).

Indian IS 875-1987 option - When this option is selected, the live load reduction method based on Section 3.2.1 of the IS:875(part2) - 1987 Standard is used. The basic formula is as follows:

Number of Floors (including Roof) to be carried by element under consideration	LLRF
1	1.0
2	0.9
3	0.8
4	0.7
5 to 10	0.6
Over 10	0.5

The RLLF factor is limited to Minimum Factor values.

Hong Kong COP 2001 option. When this option is selected, the live load reduction method based on Section 3.7.3.1 of the Hong Kong COP 2011 Standard is used. The basic formula is as follows:

Number of Floors (including Roof) to be carried by element under consideration	LLRF
1	1.0
2	0.95
3	0.90
4	0.85
5	0.80
6	0.75
7	0.70
8	0.65
Over 8	0.60

The RLLF factor is limited to Minimum Factor values

KBC 2009 option -  When this option is selected, the influence area live load reduction method based on Section 0303.4.1 of the KBC 2009 Standard is used. The basic formula is as follows:

The RRLF factor is limited to Minimum Factor values

NBCC95 option -  When this option is selected, the live load reduction method based on Section 4.1.6.9(3) of the NBCC 1995 Standard is used. The basic formula is as follows:

The RLLF factor is limited to Minimum Factor values (see bullet below).

NBCC2005  option - When this option is selected, the live load reduction method based on Section 4.1.5.9(3) of the NBCC 2005 Standard is used. The basic formula is as follows:

  

The RLLF factor is limited to Minimum Factor values (see bullet below).

NBCC2010 option - When this option is selected, the live load reduction method based on Section 4.1.5.8(3) of the NBCC 2010 Standard is used. The basic formula is as follows:

The RLLF factor is limited to Minimum Factor values (see bullet below).

UBC-97 option - When this option is selected, the live load reduction method used is similar to that described in Section 1607.5 of the 1997 UBC. The basic formula used is:

RLLF =   1 - 0.01r (A - A_min)

where,

r	=	Rate of live load reduction, 1/length2. The default value is 0.08 in 1/ft2 units.
A	=	Tributary area for the element or reaction, length2. If A does not exceed Amin then no live load reduction is used.
Amin	=	User specified minimum tributary area for the element or reaction, length2. The default for this item is 150 ft2.

The RLLF factor is limited to Minimum Factor values (see bullet below).

User Parameters (per Section 1607.5, UBC 1997) - When this option is selected, the tributary area live load reduction method based on Section 1607.5 of the 1997 UBC is used. The basic formula is as follows:

RLLF =   1 - 0.0008(A - 150)

The RLLF factor cannot be less than the Minimum Factor value.

2) Design principles :-

• One of the main structural principles is that elements such as the roof, floor and walls must remain stationary. For this to happen, there needs to be an equilibrium of forces when the forces acting on them are equal and opposite. Under loading, some deflection and deformation in the form of bending and buckling may occur, and if this movement is not allowed for then structural failure may be the result. Therefore, a principle of structures is that they be designed to maintain a state of equilibrium; resisting external loads without moving.

The study of the causes and effects of stationary forces acting on rigid objects is statics. When a structure is stationary or in equilibrium, it is a ‘static body’. For a structure to remain static, three basic equations must hold true :

1.Sum of all vertical forces must be zero.

2.Sum of all horizontal forces must be zero.

3.Sum of all bending forces, or moments, must be zero.

• Another principle is that the structure should be capable of withstanding the most severe combination of forces that are likely to be applied. This is determined by the geolocation relevant to the structure, such as in places where strong winds or heavy rain are common weather conditions.

The main types of load which a structure must be able to resist are:

1.Dead loads: Such as the fixtures and structural elements.

2.Live loads: Such as occupants, furniture, traffic.

3.Environmental loads: Such as wind, snow, earthquake, settlement.

• The effectiveness of a structure depends on the mechanical properties of the materials from which it is constructed. These properties includes Strength, Toughness, Elasticity, Plasticity, Ductility, Malleability, Brittleness, Hardness.

• Structural members are the primary load bearing components of a building, and each have their own structural properties which need to be considered. Such members include:

1.Beams: Horizontal members which transfer loads to supports.

2.Columns: Vertical members which transfer compressive loads to the ground.

3.Bracing: Members that interconnect and stiffen columns and beams.

4.Roof trusses: Load-bearing frames constructed of connected triangular shapes.

5.Retaining walls: Support soil where a sloping site requires excavation.

6.Concrete slabs: Span horizontally between supports, used as floors and sometimes as roof systems.

7.Footings: Transfer load from the structure to the foundations.

Philosophies behind “Limit States Design” :-

The philosophy of limit state design method is to see that the structure remains fit for use throughout its designed life by remaining within the acceptable limit of safety and serviceability requirements based on the risks involved.