12.4. Figure P12.4(a) shows a rigid bar AB of length L, which is pinned at B and compressed by a horizontal force P at A. The side of the bar is bonded to a block of rubber which can be modelled as an elastic foundation of modulus k, as shown in Figure P12.4(b). In other words, the rubber exerts a vertical force w(z) per unit length given by w{z) = ku(z), where k is a constant and u(z) is the local vertical displacement. Find the value of P at which the system becomes unstable. (a)

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12.4. Figure P12.4(a) shows a rigid bar AB of length L, which is pinned at B and
compressed by a horizontal force P at A. The side of the bar is bonded to a block
of rubber which can be modelled as an elastic foundation of modulus k, as shown
in Figure P12.4(b). In other words, the rubber exerts a vertical force w(z) per unit
length given by
w{z) = ku(z),
where k is a constant and u(z) is the local vertical displacement.
Find the value of P at which the system becomes unstable.
(a)
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Transcribed Image Text

12.4. Figure P12.4(a) shows a rigid bar AB of length L, which is pinned at B and compressed by a horizontal force P at A. The side of the bar is bonded to a block of rubber which can be modelled as an elastic foundation of modulus k, as shown in Figure P12.4(b). In other words, the rubber exerts a vertical force w(z) per unit length given by w{z) = ku(z), where k is a constant and u(z) is the local vertical displacement. Find the value of P at which the system becomes unstable. (a)