Reinforced Concrete Design 2: Frame Analysis

The structure is three dimensional (3D),

comprising floor slabs, beams, columns and

footings, which monolithically connected and

act integrally to resist vertical loads and lateral

loads.

3D view of reinforced concrete building structure

Idealized as 3D frame which consist of slabs, beams and column.

In many cases the slabs are analyzed separately (analyses frame consist only beams and columns)

3D frame of building structure

Analysis of 3D frame represent the real behavior

of the structure but it is quite complicated since

the structure is highly indeterminate

The analysis normally carried out by computer

since the manual calculation is unfeasible

In order to simplify the analysis, the 3D structure

is generally divided into a series of independent

parallel two dimensional plane frames (2D).

2D frame of building

structure

Simplified frame into substitude frames (sub-

frame) or continuous beams

Braced Frame ◦ 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

Unbraced Frame

◦ Frame that not 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

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.

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.

◦ The ends of the columns remote from the beams may generally

be assumed to be fixed unless the assumption of a pinned end is

clearly more reasonable

Sub-frame for analysis of beams and columns

Two-points 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.

◦ The column 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

Sub-frame for analysis of individual beam

The stiffness of the beams on either side of the beam considered should be taken as half their actual values if they are taken to be fixed at their outer ends

Continuous beam and one-point sub-frame

◦ The moments and forces in the beams at one level may also be obtained by considering the beams as a continuous beam over supports providing no restraint to rotation

Continuous beam for analysis of beams

One-point sub-frames for analysis of columns

The ultimate moments for column may be calculated by simple moment distribution procedure

assumption that the column and beam ends remote from the junction under consideration are fixed and that the beams posses half their actual stiffness

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

Action on buildings is due to permanent (dead load),

variable (imposed, wind, dynamic, seismic loads)

and accidential load

Mostly multistiry buildings for office or residential

purpose are design for dead, imposed and wind

loads

Separate actions must be applied to the structure in

appropiate directions and various tyoes of actions

combined with partial safety factors selscted to

cause the most severe design condition.

The framing plans for a

multistory building are shown

in Fig E9.1. The main

dimensions structural features,

loads, material, etc. are also

set out in the figure. 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 that

discussed before

Building frames are subjected to lateral loads as

well as vertical loads.

Building must not only have sufficient lateral

resistance to prevent failure but also must have

sufficient resistance to deflection to prevent

damage to their various part.

Portal method ◦ The frame theoretically divided into independent portals.

◦ The shear in each storey is assumed to be divided between the

bays in proportion to their span.

◦ Shear in each bay is then divided equally between columns.

◦ The column end moments are the column shear multiplied by

one-half the column height

◦ Beam moment balance the column moments

◦ The external column only resist axial load which is found by

dividing the overturning moment at any level by the width of the

building

Cantilever method

◦ The axial loads in column are assumed to be

proportional to the distance from the center of

gravity of the frame

◦ Assume that all the column in a storey are of

equal cross-section area and the point of

contraflexures are located at the mid-points of

all column and beams.

Wind forces- variable loads which act directly on

the internal and external surfaces of structures.

The intensity is related to the square of the wind

velocity and the dimension of the members that are

resisting the wind.

Wind velocity-dependent on geographical location,

the height of the structure, the topography of the

area and the roughness of the surrounding terrain.

The response of a structure to the variable

action of wind can be separated into two

components

Background component ◦ Involves static deflection of the structure under the wind pressure

Resonant component ◦ involves dynamic vibration of the structure in response to

changes in wind pressure

Wind

◦ creates pressure on the windwards side of a building

and suction on its other three sides

◦ Produces suction on flat roofs, on the leeward side of

sloping roofs, and even on the windwards side of roofs

with a pitch less than 30°

Simplified procedure ◦ Limited in application to building of rectangular in

plan and not greater than 15.0 m high

Analytical procedure

◦ Limited to regular building that are not more

than 200m high and structure with roof span

less than 100 m

Wind tunnel procedure

◦ Used for complex buildings