Fixed End Moment

By Mukul Yadav|Updated : October 6th, 2022

The fixed end moment is the end moment of a structure, which provides restraint to the end support of members. In civil engineering, structural analysis, there are mainly two methods of analysis: the fixed method of analysis and the displacement method. Both methods of analysis are used to find out the unknown parameters of analysis. In the force method of analysis, forces are considered to be unknown, and in the displacement method, displacement is considered to be unknown. The concept of fixed end moment is used in the moment distribution method of analysis which is one of the force methods of analysis.

Fixed End Moment Notes PDF

Fixed end moment has many applications in structural analysis; It is used to calculate the deflection of a beam under the action of external loading. Fixed end moment is also used to establish the slope deflection equation for a structural member, which is used to find deflections in beams. The fixed end moment of a structural member will depend on many parameters like type of support, loading condition, etc.

What is Fixed End Moment?

The fixed end moment is the end resiting moment of a member induced over the fixed support. It is used to find out the variation of moments along the span of members. In the moment distribution method of analysis, the fixed end moment is calculated, then balanced for any support.

Variation of fixed end moment over the member is represented by a diagram known as the fixed end moment diagram. This diagram can be of any shape, depending on the loading and support condition of the member. The fixed end-moment diagram always varies linearly because it contains only the end values.

Fixed End Moment Formula

The formula for fixed end moment will depend upon the many parameters like variation of load over the member and type of supports. Questions based on the fixed end moment formula are an important part of the GATE question papers. It will not depend upon the beams' cross-sectional properties or material properties. A fixed end moment in the beam will generate when an external load is applied over it.

Fixed End Moment Table

Here values of fixed end moments of some beams are given in the tabular form, which will help to solve the questions.

Fixed End Moment Table:

Fixed End Moment Equations

Fixed end moment values are subject to the external loading and beam dimensions like the length. So, it can be calculated only after knowing these parameters. These fixed-end moment values will help find the slope deflection equations used to calculate the deflection in beams.

Fixed end moment equations are the equations that are used to calculate the value of fixed end moments. These equations are the function of load intensity and the length of the beam. In the case of differential settlement of the beam, it also depends on the deflection. Fixed end-moment equations are important for the upcoming GATE exam.

Here few slope deflection equations depend upon fixed end moment values.

Fixed End Moment Equations

Fixed End Moment for Continuous Beam

As we discussed, that fixed end moment value depends on the type of loading and its intensity irrespective of the beam type. It can be calculated only after knowing the value of loading intensity. So, let’s consider first a continuous beam having a uniformly distributed load.

A continuous beam is a beam having more than one support. For the purpose of analysis, the intermediate support of the continuous beam is treated as the fixed support, and an end portion of such beam is considered the propped cantilever beam. So, the fixed end moment for the continuous beam subjected to UDL can be calculated by considering the fixed beam and propped cantilever beam accordingly.

Nature of Fixed End Moment for a Fixed Beam

A fixed beam is a beam that has fixed support at both ends, and fixed end moment values will depend on the loading over the span of the beam. Generally, the nature of fixed end moment at the fixed end is hogging in nature, which creates tensile stress on the top of the beam.

Here some fixed end moment values for different loading conditions on a fixed beam are given:

Nature of Fixed End Moment for a Fixed Beam

Difference between Fixed End Moment and Bending Moment

The bending moment will generate when a structure is subjected to external loading. It is the effect of transverse loading over the member of a structure. Fixed end moment and bending moment both cause the bending effect over the member, But the effect of both may be different for the beams, which depends on the loading conditions and support conditions of beams. These differences will help clear these concepts from the GATE CE syllabus.

Here a few difference is provided between these moments.

  • Fixed end moment itself, a bending moment just its cause is different.
  • The fixed end moment only generates at the end support of the beam, but the bending moment can occur throughout the whole span.
  • The fixed end moment generates due to the resistive property of the supports, while the bending moment is due to the resistive property of the member itself.

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Fixed End Moment FAQs

  • The fixed end moment is the resistive moment offered by the beam's support, which generates due to the external loading applied.

  • Fixed end moment is developed due to the external loading, depending on the type of loading and type of support. It will not depend on the cross-sectional parameters of the member.

  • Calculation of fixed end moment will depend on the number of total redundant forces in the member. And it can be calculated with the help of available equilibrium equations and compatibility conditions of members.

  • As the fixed end moment, itself a bending moment, its unit will be the same as the unit of the bending moment, and that will be the N-m.

  • Carry-over moments are the moments transferred from the near end of a member. In a member at a joint, the moment will be transferred according to their stiffness factor.

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