Abstract
The notion of shear-force (or shear) and bending-moment diagrams was introduced by means of some examples in Sect. 2.4. Knowledge of the distribution of shear force and bending moment in a beam is essential for the determination of the stresses and the deflection of the beam. For this reason, the calculation of these diagrams is developed here systematically on the basis of differential equations of equilibrium analogous to Eq. (6.75) for axial forces.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
This w should not be confused with the same symbol used to denote displacement in the z-direction in Sect. 5.3.
- 2.
Named for two noted Swiss mathematicians, Daniel Bernoulli (1700–1782) and the aforementioned (page 55) Leonhard Euler, who developed it around 1750, though engineers did not get around to using it for another century.
- 3.
A better measure of slenderness than the span-to-depth ratio is the slenderness ratio, which will be discussed in the next chapter.
- 4.
Discorsi e Dimostrazioni Matematiche, intorno á Due Nuove Scienze (Discourses and Mathematical Demonstrations Concerning Two New Sciences) was published in 1638.
- 5.
This derivation relies on the identity \(d{(\tan}^{-1}x)/dx = 1/(1 + {x}^{2})\).
- 6.
Since the beam is assumed to behave locally as if it were in pure bending, the cross-section is assumed to be perpendicular to the deflection curve, and therefore the inclination θ of the latter is also the rotation of the cross-section. This assumption is, however, an approximation.
- 7.
Émile Clapeyron (1799–1864) was a French engineer and physicist.
- 8.
George Green (1793–1841) was a British mathematical physicist.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Lubliner, J., Papadopoulos, P. (2014). Elastic Bending of Beams. In: Introduction to Solid Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6768-7_8
Download citation
DOI: https://doi.org/10.1007/978-1-4614-6768-7_8
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-6767-0
Online ISBN: 978-1-4614-6768-7
eBook Packages: EngineeringEngineering (R0)