CHAPTER 2 STRUTS Summary The allowable stresses and end loads given by Euler's theory for struts with varying end conditions are given in Table 2.1. Table 2.1. End condition Fixed-free Pinned-pinned Fixed-pinned Fixed-fixed (or rounded) π2E1 T2El 2π2E1 4π2E1 4L2 L2 L2 L2 Euler load Pe or,writing /=Ak2,wherek=radius of gyration π2EA R2EA 2π2EA 4n2EA 4(L/k)2 (L/k2 (L/k) (L/k)2 Euler stress n2E nπ2E 2π2E 4n2E 4(L/k)2 (L/k2 (L/k)2 (L/k)2 Here L is the length of the strut and the term L/k is known as the slenderness ratio. Validity limit for Euler formulae where C is a constant depending on the end condition of the strut. Rankine-Gordon Formula Oy O= 1+a(L/k)2 where a=(o/2E)theoretically but is usually found by experiment.Typical values are given in Table 2.2. Table 2.2. Material Compressive yield stress (MN/m2) Pinned ends Fixed ends Mild steel 315 1/7500 1/30000 Cast iron 540 1/1600 1/64000 Timber 35 1/3000 1/12000 N.B.The value of for pinned ends is always four times that for fixed ends 28CHAPTER 2 STRUTS End condition Summary Fixed-free Pinned-pinned Fixed-pinned Fixed-fixed T~EI X~EI 2n2EI 4n2EI 4L2 L2 L2 L2 (or rounded) ~ ~ ~ ~ The allowable stresses and end loads given by Euler’s theory for struts with varying end conditions are given in Table 2.1. Table 2.1. Euler load P, I or, writing I = Ak2, where k = radius of gyration Here L is the length of the strut and the term L/k is known as the slenderness ratio. Validity limit for Euler formulae where C is a constant depending on the end condition of the strut. Rankine -Gordon Formula *?, o= 1 + U(L/k)* where a = (o,./n2E) theoretically but is usually found by experiment. Typical values are given in Table 2.2. Table 2.2 Material Cast iron Timber Compressive yield stress Pinned ends Fixed ends 1/7500 1 /30 000 1 /64 000 1/12000 N.B. The value of II for pinned ends is always four times that for tixed ends 28