Question
Download Solution PDFA simply supported beam carries a point load (w) at the centre. The flexural stiffness of the beam is if the span is (l) :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Flexural stiffness:
- The bending stiffness (k) is the resistance of a member against bending deformation.
- It is a function of the Young's modulus E, the second moment of area I of the beam cross-section about the axis of interest, length of the beam and beam boundary condition.
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Bending stiffness of a beam can analytically be derived from the equation of beam deflection when it is applied by a force. (i.e. \(K=\,\frac{w}{\Delta}\) ).
solution:
For a simply supported beam carries a point load (w) at the centre, deflection at center \(\Delta =\,\frac{wl^3}{48EI}\)
∴ Bending or flexural stiffness, \(K=\,\frac{w}{\Delta}\) ⇒ \(K=\,\frac{w}{\frac{wl^3}{48EI}}\,=\,\, \frac{48EI}{l^3}\)
Last updated on Jan 29, 2024
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