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Continuous Beams

Eng. Loai Tarabulsi

Introduction

• Reinforced concrete building construction commonly has floor slabs, beams girders and columns continuously placed to form a monolithic system.

 Reinforced concrete structures are generally monolithic or continuous and, thus, statically indeterminate.

A load placed in one span of a continuous structure will cause shears, moments, and deflections in the other spans of that structure

• The individual members of a structural frame must be designed for the worst combination of loads that can reasonably be expected to occur during its useful life.
• Dead loads are constant , live load such as load from human occupancy can be placed in various ways , which will result in large effects than others.

• The determination of these internal forces in continuously reinforced concrete structures is usually based on elastic analysis of the structure at factored loads.
• Before failure reinforced concrete section are usually capable of considerable inelastic rotational at nearly constant moment.
• This permits a redistribution of elastic moments and provides the basis for plastic analysis of beams, frames , and slab

Envelope diagrams

Approximate Method

ACI coefficient method of analysis

• approximate method (also called coefficient method) is used for the analysis of continuous beams, ribs and one-way slabs.
• It allows for various load patterns where live load is applied on selected spans and maximum shear force and bending moment values are obtained by the envelope curves.
• This simplified and approximate method allows also for the real rotation restraint at external supports, where the real moment is not equal to zero.

• Elastic analysis gives systematic zero moment values at all external pin supports.
• The coefficient method is thus more realistic but is only valid for standard cases.

• l n is the clear length of the span For internal negative moment, l n is the average of clear lengths of the adjacent spans
• The next figure gives the ACI terminology for the various spans, support and support faces

• Case (a): This case corresponds to an external support not integrated with the beam. This occurs for instance when the beam is supported by a precast column
• Case (b) and Case (c): These are standard situations with two spans (c) or more than two spans (b).
• The moment coefficient at the external support depends on the type of support