Beam Deflections Analysis

Serviceability of a structure is determined by its deflection, cracking, extend of corrosion, and surface deterioration. Excessive deflection of a beam or slab can damage a partition below, and excessive deflection of a lintel beam above a window opening can crack the glass panes.

The program computes the maximum deflection of a simply supported double-reinforced concrete rectangular or T beam under the action of service loads, taking into account the immediate and the long-term effects, according to ACI design criteria. In addition, continuous beams or one-way slabs may also be modeled by entering the corresponding end moments.

Example

Find the maximum deflection of a uniformly loaded continuous beam with four spans of 36 ft., a width of 14 in. and a total depth of 21-in. supporting a 4" slab. The steel area is 4.00 in2 at a depth of 18.25 in. The beam is subjected to a service dead load of 700 plf including its self-weight and a live load of 1200 plf. Use f'c = 4 ksi and fy = 60 ksi. Assume that 50% of the live load is continuously applied.

Input Data

The required input data consists of the materials' properties and beam dimensions. In addition, the service dead and live loads (a distributed load and two end moments) are required, as shown schematically in the figure below.

Procedure

The program computes the section's properties in the pre-cracking and post-cracking stages and calculates the effective moment of inertia based on the Branson approach.

The maximum deflection is computed as the sum of the instantaneous deflection and the long-term deflection in accordance with the ACI procedure. It is then compared with maximum values allowed, depending on the type of structure.

ASDIP generates the bending moment diagram of the designed beam for the specified service loads, as shown below.

Output

Figure below shows the template related to this module with the example problem's data. In this example, the code deflection criterion is met by conditions A and B only. Therefore, the continuous beam is limited to floors or roofs not supporting or attached to nonstructural elements such as partitions.