Chapter 2.0 - Frame Analysis

BFC32803

BFC32803

Reinforced Concrete Design II

Reinforced Concrete Design II

Frame Analysis

Frame Analysis

Dr. Zainorizuan Mohd Jaini

Dr. Zainorizuan Mohd Jaini

[email protected]

[email protected]

Learning Outcome

Learning Outcome

 At the end of this chapter

 At the end of this chapter, students should be able , students should be able to:to: 1)

1) AnaAnalyslyse the e the resresponponses oses of buf buildilding ing (sh(shear ear forcforce and e and benbendindingg moment) subjected to combined vertical actions and wind moment) subjected to combined vertical actions and wind load.

load.

(C4-PLO4) (C4-PLO4) 2)

2) ManManipuipulatlate stre structucturaural desl design pign procrocessesses to ces to compompletlete thee the assigned project.

assigned project. (P4-PLO2)

(P4-PLO2) 3)

3) ReReporport dest design wign workorks whis which coch comprmprise oise of idef ideas aas and pnd probroblemlem solving through suitable tools or

solving through suitable tools or methodsmethods (A3-PLO3)

Introduction

Introduction

 The building structure is 3D, comprising floor slabs, beams,The building structure is 3D, comprising floor slabs, beams, columns and footings, which monolithically connected and act columns and footings, which monolithically connected and act integrally to resist vertical/lateral loads.

integrally to resist vertical/lateral loads.

 In the design, it has to analyze the structure subjected to allIn the design, it has to analyze the structure subjected to all probable combinations of loads, considering the ultimate limit probable combinations of loads, considering the ultimate limit state.

state.

 Once the bending moment, shear force etc. were obtained,Once the bending moment, shear force etc. were obtained, reinforcements can be designed according to the standard.

reinforcements can be designed according to the standard.

 Generally, 3D wide frame analysis is the most accurate methodGenerally, 3D wide frame analysis is the most accurate method to analyse the frame building

Introduction

Introduction

 3D frame is complex and need to be carried out using relevant computer software such as StaadPro, ESTEEM, ETABS, etc.

 However, in many cases the slabs are analyzed separately.

 Thus, the analysis may be simplified to appropriate sub-frame, consist only beams and columns.

Introduction

 However, in many cases the slabs are analyzed separately.

 Thus, the analysis may be simplified appropriately sub-frame, consist only beams and columns.

3D frame which consist of

slabs, beams and column simplified

3D frame consist only beams and columns

Introduction

 In order to simplify the analysis, the 3D structure is generally divided into a series of independent parallel 2D plane frames.

Sub-Frames

 2D plane frame can be further simplified into 3 level sub-frames:

i) Complete sub-frame

The frame consists of all beams at each level with columns top and bottom of beams. Moments at columns and beams are tabulated by analyzing the complete sub-frame.

ii) Simplified sub-frame

The frame consists of a selected beam with columns and neighbouring beams at both sides of selected beam.

iii) Simplified sub-frame at point

The frame consists of a selected point or node with columns at top and bottom, and neighbouring beams coming into the point.

Sub-Frames

 2D plane frame >>> complete sub-frame:

 A B C D E  A B C D E Second floor First floor Roof Complete 2D Frame

Sub-Frames

 Complete sub-frame >>> Simplified sub-frame:

 A B C D E Second floor First floor Roof  A B C D  A B C Complete 2D Frame

Sub-Frames

 Simplified sub-frame >>> One point sub-frame:

 A B C D E Second floor First floor Roof  A B _{B C D} Complete 2D Frame

Type of Frame

1) Braced Framed (BF)

Frames that not contribute to the overall stability of the structure.

None of the lateral actions, including wind, are

transmitted to the columns and beams but carries by bracing members such as shear wall.

Support vertical actions only.

Type of Frame

2) Unbraced Framed (UBF) Frame that contribute to the overall stability of the

structure.

 All lateral actions, including wind, are transmitted to the columns and beams since there are no bracing

members such as shear wall are provided.

Support vertical and lateral actions

Method of Analysis

 Primary objective: to obtain a set of internal forces and moments throughout the structure that are in equilibrium with the design loads for

the required loading

combinations.

 General provisions to analysis are set out in EN 1992-1-1 Section 5.

Vertical load Vertical load + Horizontal load Load transfer from slabs to beams Load transfer from slabs to beams ; wind to column Design action patterns:

maximum-minimum

Moment distribution method

Fixed end moments, Shear forces, Bending moments

General Consideration

 General consideration for sub-frame analysis:

i) Method of sub-frame analysis can be conducted using one-level sub-frame, two-point sub-frame or one-point sub-frame with continuous beam.

ii) The column or/and beam ends remote from the beam under consideration may generally be assumed to be fixed unless the assumption of pinned is clearly more reasonable.

iii) Stiffness for interior beam is K_B.

iv) Stiffness for fixed end (beam elements) posses half their actual stiffness, 0.5KB.

v) The arrangement of the design ultimate variable loads should be such as to cause the maximum moment the column.

Method of Analysis

 One-level sub-frame

Each sub-frame mat be taken to consist of the beams at one level together with the columns above and below.

 At least four cases combination of actions: [Max][Min][Max]; [Min][Max][Min]

[Max][Max][Min]; [Min][Max][Max]

Method of Analysis

ii) Two-point sub-frame

The moments and forces in certain individual beam may be found by considering a simplified sub-frame consisting only of the beam, the columns attached to the end of that beam and the beams on either side is any.

Load at interior beam where stiffness = K_B  is always for maximum design load.

Method of Analysis

iii) One-point sub-frame with continuous beam

The moments and forces in the beams at one level 

considering the beams as a continuous beam over supports providing no restraint to rotation.

The ultimate moment for column   simple moment

distribution procedure

Combination of Actions

 Action on buildings is due to permanent (dead load), variable (imposed, wind, dynamic, seismic loads) and accidental load.

 Mostly multistory buildings for office or residential purpose are design for dead, imposed and wind loads.

 Separate actions must be applied to the structure in appropriate directions and various types of actions combined with partial safety factors selected to cause the most severe design condition.

 Maximum design load = 1.35G_k + 1.5Q_k

 Minimum design load = 1.35G_k

 Wind load = 1.2W_k

Combination of Actions

 For the combination of dead load and imposed load, the following loading patterns are considered:

Braced frame 1) All spans loaded with maximum dead plus

imposed loads

2) Alternate spans loaded with maximum dead load and imposed load and all other spans loaded with minimum dead load

Unbraced frame 1) Three cases loading arrangements as

braced sub-frame

2) Vertical actions for sub-frame 3) Wind load for complete frame

Analysis of Braced Frame

 Procedure:

1. Analyse all actions, maximum and minimum design loads 2. Calculate moment inertia, I = bh3 _/12

3. Calculate stiffness of beams and columns, k = I/L 4. Determine distribution factor, DF = k_i / Σk

5. Determine fixed end moment (FEM) of beams 6. Perform moment distribution by cases:

a) Case 1 [Max][Max][Min] b) Case 2 [Min][Min][Max] c) Case 3 [Max][Min][Max] d) Case 4 [Min][Max][Min]

7. Calculate actual shear force and bending moment 7. Draw BMD and SFD diagrams

Wind Loading

 Wind forces are variable loads which act directly on the internal and external surfaces of structures.

 The intensity of wind load on a structure is related to the square of the wind velocity and the dimension of the members that are resisting the wind.

 Wind velocity is dependent on: a)Geographical location

b)The height of the structure c) The topography of the area

Wind Loading

 The response of a structure to the variable action of wind can be separated into 2 components:

Background component Resonant component

- Involves static deflection of the structure under the

wind pressure

- Involve dynamic vibration of the structure in response to changes in wind pressure

- Relatively small and structural response to wind forces is

usually treated using static method of analysis.

- Example: Natural wind - Example: High-fluctuate wind, hurricane, micro-burst,

Wind Loading

 Wind creates pressure of the windward side of a buildings and suction on three sides.

Effect of Wind

Hurricane Sandy batters New York with howling winds

Building failure due to high pressure wind from Hurricane Katrina

Wind Analysis

 Three procedures are specified in MS 1553:2002, Malaysian Standard for the calculation of wind pressures in buildings:

1) The simplified procedure:

Limited in application to building of rectangular in plan and not greater than 15 m high

2) The analytical procedure:

Limited to regular buildings that are not more than 200 m high and structure with roof spans less than 100 m

3) The wind tunnel procedure: Used for complex building

Wind Analysis

 Simplified procedure (MS1553 Appendix A)

 

2



,



2





0.613 _{s z cat pe pi}  

p  V M C  C  

where:

= The design wind pressure in Pa = The basic wind speed (Figure A1)

= The terrain/height multiplier (Table A1)

= The external pressure coefficient for surface of enclose building ( A2.3 and A2.4)

= The internal pressure coefficient for surface of enclose

building which shall be taken as +0.6 or -0.3. The two cases shall be considered to determinate the critical load requirements for the appropriate condition.

p  s  V   , z cat  M  pe  C  pi  C 

Wind Analysis

 Analytical procedure(MS1553 Section 2)





2

0.613 _{des fig dyn}  

p  V C C  

where:

= = The design wind speed

= Importance factor (Table 3.2)

= Site wind speed

= Basic wind speed 33.5m/s for zone I and 32.5m/s for zone 2 (refer Figure 3.1)

= Wind directional multiplier = 1.0 = Terrain/height multiplier (Table 4.1)

= Shielding multiplier (Table 4.3) equal to 1.0  if the effects of shielding are ignored or not applicable.

des  V   l  , sit s d z cat s h   V V M M M M   s  V   d  M  , z cat  M  sit  V l  s  M 

Wind Analysis

= Hill shape multiplier. Shall be taken as 1.0 except that for particular cardinal direction in the local topographic zones.

= Aerodynamic shape factor for external pressure.

= External pressure coefficient ( Table 5.2.a and 5.2.b) for windward and leeward walls respectively for rectangular enclosed building

= Area reduction factor, combination factor, local

pressure factor and porous cladding reduction factor respectively. All shall be taken as 1.0 in most cases. = Dynamic response factor. Shall be taken as 1.0 unless the

structure is wind sensitive.

h  M  1 fig pe a c p   C  C K K K K     pe  C  1 a c p  K K K K     dyn  C 

Wind Analysis

Analysis of Unbraced Frame

 Procedure:

1. Calculate design wind load, W_d=1.2W_k

2. Calculate lateral point load at each level of frame a) Assume contraflexure point at center of frame

b) Axial loads in column are in its proportion to distances from the centre of gravity of frame

c) All columns are equal cross-section area 3. Lateral load analysis using Cantilever Method.

- Calculate axial force in columns, then shear force in beams and columns from top to ground levels.

4. Vertical load analysis due to wind, 1.2 G_k + 1.2Q_k - analysis of one level sub-frame

Analysis of Unbraced Frame

 Lateral load of wind load +  Vertical load due to wind pressure  A₁ B₁ C ₁ D₁  A₂  B₂  C ₂  D₂   A₃ B₃ C ₃ D₃  A₁ B₁ C ₁ D₁  A₂  B₂  C ₂  D₂   A₃ B₃ C ₃ D₃ 1.2W _K 1.2W _K 1.2W _K 1.2W _K 1.2G_K+1.2Q_K 1.2G_K+1.2Q_K 1.2G_K+1.2Q_K

Tutorial

1) The framing plans for a multistory building are shown in the layout. Analyze sub frame 3/A-D, Level 1 to determine shear forces and bending moments of corresponding beams and columns. Use all the three methods of analysis. Given the following data: Permanent office building (Design life 50 years); Location: Near sub-urban (Zone 1 of Malaysia wind speed mapping), Topography: Flat area –slope<0.05 (Building around within 1 KM radius); Beam in grid line 1,2,3…12: 250x600mm, Beam in grid line A, B, C & D: 250x500mm; Slab thickness = 150mm; Columns: 300x400mm; Imposed load: 4.0kN/m2_,

finishes, ceiling, services etc: 0.75kN/m2_{, Partitions: 0.5 kN/m}2_.

Tutorial

2) The framing plans for a multistory building are shown in the layout (download here). Given the following data: Permanent office building (Design life 50 years); Location: Near sub-urban (Zone 1), Topography: Flat area-slope<0.05 (Building around within 1 KM radius); Beam in grid line 1,2,3…12: 250x600mm, Beam in grid line A, B, C & D : 250x500mm, Slab thickness = 150mm, Columns: 300x400mm; Imposed load: 4.0kN/m2_,

Finishes, ceiling, services etc: 0.75kN/m2_{, Partitions: 0.5kN/m}2_.

For the multistory building:

a) Calculate the wind load on the building

b) Calculate the bending moments for all beams and columns, due to wind load

c) Analyse the subframe consisting Beam 3/A-D, Level 1 with the column above and below then, subjected to vertical load only.