Beam Fixed at Both Ends and subjected to nonuniform bending

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SUMMARY

A beam fixed at both ends and subjected to nonuniform bending experiences complex stress distributions. The upper section of the beam can be both in compression and tension depending on the specific moment diagram. This scenario is classified as a statically indeterminate problem, requiring an analysis of the deformed shape to accurately determine the stress states. Understanding the moment diagram is crucial for identifying which parts of the beam are in tension and which are in compression.

PREREQUISITES
  • Understanding of statically indeterminate structures
  • Familiarity with moment diagrams in structural analysis
  • Knowledge of beam deformation and compatibility conditions
  • Basic principles of mechanics of materials
NEXT STEPS
  • Study the principles of statically indeterminate structures
  • Learn how to construct and interpret moment diagrams for beams
  • Explore the concepts of beam deformation and compatibility
  • Review the mechanics of materials, focusing on stress and strain analysis
USEFUL FOR

Structural engineers, civil engineering students, and professionals involved in analyzing beam behavior under various loading conditions.

UMath1
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If a beam is fixed at both end and subjected to nonuniform bending would the upper section of the beam still be in compression. My intuition and free body diagrams suggest it would but geometrically in this case, wouldn't all sections of the beam, even the upper section, have to elongate/curve in order to maintain compatibility with the fixed joints?
 
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You need to look at the moment diagram for this beam; that will tell you what parts are in tension and what parts are in tension. This is a statically indeterminate problem. Think about the deformed shape and that will tell you that parts of the upper edge are in tension and part in compression.
 

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