Beam Deflection Theory

Abstract

There are numerous types of beams that are fixed at either one or both ends such as supported, fixed, cantilever, truss, etc. With the aid of Abaqus, we can simulate the deflection of a simply supported bridge with a vehicle at the mid-span and obtain the maximum deflection from the simulated result. Manual calculation was also required to obtain the maximum deflection of the loaded bridge by using beam deflection theory. The span/deflection ratio must be within 200 to 400, and percentage difference must be below 10%.

Table of Contents

Introduction 4

• Objective 4

Problem Definition / Design Requirement 4

• Schematic Diagram 4

Methods 5

• Assumptions 5

• Input file into Abaqus 5

• Analytical Solution 6

Span/Deflection Ratio: 6

Next, to use both Abaqus and manual calculations to calculate the maximum deflection allowed in the beam. Last, is to compare the results obtain to achieve a percentage error difference of within 10%.

Problem Definition / Design Requirement

As we are required to work with a UDL over a supported beam, we are unable to model the deformation of the beam. However, we can use symmetry boundary condition to apply onto the beam. The span/deflection ratio must be within 200 to 400 which can be achieved by taking into account the uniform distributed load of the bridge/beam.

• Schematic Diagram Length of the Vehicle = 6.1 meters.

Weight of the Vehicle =76 tons = 76 000kg x 9.81 =745560N

Length of the beam = 37 meters.

R1 and R2 are the reaction forces.

The bridge is subjected to Uniformly Distributed Load (UDL), and the truck is also subjecting the bridge to UDL at its mid-span.

Methods

• Assumptions

Summation of forces at axis 2 is equal to zero: &

Take in consideration:

Young’s Modulus, E = (200*10⁹)

Gravity = 9.81 m/s

Volumetric ρ = 7800 kg/mᶟ

Linear ρ = 7800*A

• Input file into Abaqus

*HEADING

BEAM BRIDGE DESIGN

*NODE, NSET=ALLN 1, 0 2, 15.45 3, 18.5

*ELEMENT, TYPE=B23, ELSET=ALLE 1, 1, 2 2, 2, 3

*BEAM SECTION, ELSET=ALLE, SECTION=BOX,