Download PDF by Ian McDonagh (Auth.): Mechanical Science for Technicians. Volume 1

By Ian McDonagh (Auth.)

ISBN-10: 0713135115

ISBN-13: 9780713135114

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Extra resources for Mechanical Science for Technicians. Volume 1

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L. L. 10kN/m t I I , JOOmrn ν««λ««α =r 2m 2m (20 + yaF)kN (20 + V4F)kN Section XX Fig. 30 By inspection of fig. 30, reaction at A = reaction at B = 4-[(10kN/mx4m)+FkN] = (20 + ^F)kN At mid-span, M = Σ moments to left of mid-span = [(20 + γ/OkN x 2m] - [(10kN/m x 2 m) x 1 m] = (20+F)kNm or ( 2 0 + F ) x 103Nm 59 From the simple bending equation, M = oily o = 200MN/m2 = 200 x 106N/m2 where / = 16 x 106mm4 = 16 x 10' 6 m 4 and :. e. 67 kN. e. when the value of y is a maximum. Thus, at any section, a max.

At the point C,x = 4 Λ ßc = ( 8 5 - 2 0 x 4 ) k N = 5 kN (upwards) Consider section DE (fig. J1l iE (x-2)m 125kN | Ί 8m 155kN 1 Fig. e. e. between D and E the shear force will change uniformly with JC, producing a straight line having a slope or gradient of 20kN/m as shown in fig. 9, the SF diagram. Referring to fig. 9, notice how the shape of the SF diagram is affected by the reactions and the loading on the beam. At A the reaction (RA = 125kN)is acting upwards, causing the shear force to increase from zero to 125 kN.

27(b). ), the tensile stress increases from zero (at the neutral axis) to σ^ Below the neutral axis, the compressive stress increases from zero (at the neutral axis) to oc. External bending moment M External bending moment Af (b) Fig. 27(a) shows the distribution of bending stress across the section of the beam in fig. 27(b) due to the external bending moment M. Consider the force 6Fi acting on the area6i41 at distance^! e. 6Fx = σ,δ^! From fig. 27(a), σ χ = — y\ yx yx and total force Fx = ZÔF, = ^Xyx6Ax Also, the force acting on area SA2 at distance y2 below the neutral axis is given by bF2 = o2 6Α2 but o2 = - ^ y2 = — y2 yc Λ (since - !

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Mechanical Science for Technicians. Volume 1 by Ian McDonagh (Auth.)


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