А 2m E 10 kN/m 2m Support settles 1 mm to right under load С 2m Figure 1 CHARACTERISTIC VALUES FOR DESIGN-F-GRADES-BENDING AND SHEAR FOR BEAMS, TENSION, COMPRESSION AND ELASTIC MODULI PARALLEL TO GRAIN Characteristic values, MPa Tension parallel to Short duration Shear Compression Short duration average modulus of elasticity parallel to the grain, MPa Stress grain average modulus of rigidity, MPa Bending parallel to grain in grade Hardwood Softwood beam Gs) Ge) (E) (G) 42 21 500 F34 84 51 6.1 63 430 1 230 67 42 34 5.1 51 18 500 F27 F22 55 34 29 4.2 42 16 000 1070 22 3.6 F17 42 25 34 14 000 930 12 000 22 19 3.3 27 800 F14 36 F11 31 18 15 2.8 22 10 500 700 F8 22 13 12 2.2 18 9 100 610 F7 18 11 8.9 1.9 13 7 900 530 6 900 F5 14 7.3 1.6 11 460 F4 12 7 5.8 1.3 8.6 6 100 410 Figure 2. Timber properties
A rigid beam ABC is supported at C by a pin support, and at A and B by timber struts AD and BE which are in turn supported by pin supports at D and E respectively (Figure 1). The struts AD and BE are constructed using F11 timber (refer Figure 2) with square cross section 40 mm x 40 mm. A uniformly distributed load of 10 kN/m acting horizontally to the right is applied along the complete length ABC. Under the action of this load, in addition to any changes in the lengths of the struts, the pin support at C settles by 1 mm to the right.
Assume that the beam and struts are weightless and that the struts will not buckle.
(a) Using equilibrium and compatibility considerations determine the support reactions at C, D and E. Hint: Since the struts AD and BE can transfer only axial force, the reactions at D and E act horizontally (that is, there are no vertical reaction components at D and E).
(b) Find the normal stress, normal strain and change in length of strut AD.
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