IntermediateTopic 58 of 106Engineering Mechanics
Statically indeterminate beams
Need compatibility of deformations in addition to equilibrium.
In depth
When reactions exceed equilibrium equations, add compatibility conditions on deflection (e.g. zero deflection at an extra support). Examples: propped cantilevers and continuous beams. They are stiffer and have lower peak moments than determinate ones.
Key points
- Degree of indeterminacy = unknowns - equations
- Force and displacement methods
- Settlements induce stresses
ExampleA fixed-fixed beam with UDL has end moments wL²/12.
Indeterminate beams have more supports than equilibrium equations, so they are often stronger and stiffer, but they need deformation checks.
What is Statically indeterminate beams?
Need compatibility of deformations in addition to equilibrium.
Why is it important to understand statically indeterminate beams?
Indeterminate beams have more supports than equilibrium equations, so they are often stronger and stiffer, but they need deformation checks.
Why are continuous beams more efficient?
The moment peaks are reduced compared with simply supported spans, so less material is needed for the same load.
How do I solve an indeterminate beam?
Use compatibility of deformations, such as the superposition method or the force method, along with equilibrium.
How is Statically indeterminate beams used in practice?
Typical applications include designing a continuous floor beam over several columns, checking the reaction distribution in a multi-span bridge girder and analysing a fixed-end beam used in a rigid frame.
What should I learn before Statically indeterminate beams?
Study "Beam deflection" first (topic 57 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
What are the key points of Statically indeterminate beams?
Degree of indeterminacy = unknowns - equations. Force and displacement methods. Settlements induce stresses.
Can you give an example of Statically indeterminate beams?
A fixed-fixed beam with UDL has end moments wL²/12.
What comes after Statically indeterminate beams?
The next topic is "Shear stress in beams", which builds directly on this one.
How difficult is Statically indeterminate beams?
It is classed as Intermediate in Engineering Mechanics (topic 58 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.