only part b not part a QUESTIONS (a Calculate the forces in the columns A, B and

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only part b not part a

QUESTIONS (a Calculate the forces in the columns A, B and C for the structure shown in Figure 8(a0. The loads are acting on the rigid bar which remains horizontal during loading. All columns are made of the same matenal. For columns A and C, the cross-sectional area is each 31000mm? while for column Bis 70000mm Assume that the forces in columns A and Care equal. (5 marks 100 kN 100 kN Figure 8(a) Rigid bar 4m 4m. 4m. A continuous beam ABC subjected to a UDL of 10kNm shown in Figure 8(b is simply supported at A and C. The mid-point at B of the beam is also supported by a column BD with the following properties: Young's modulus E 2000 Nmm cross-sectional dimensions 50mmx50mm, length 4m. If the column BD is modelled as a spring, prove that the spring constant k of the column is 1250kN/m. (1 mark) (4 marks Properties of beam ABC: EI 8x1012 Nmm 100 kN/m. 10 kN/m C A B k spring constant 5 m 5 ma Figure 8(b) Useful Information Deflection y at any pointxfrom support is w Nmma 24EI 3L' 4xt 48ET Page 9 of 10

Explanation / Answer

b) 1) using the given formula for deflection

y = -wx(x^3-2Lx^2+L^3)/(24EI)

at the distance L/2 deflection will be

y = -w*(L/2)*(L^3/8 - 2*L*L^2/4 + L^3)/(24EI)

= -w(L/2)*(5L^3/8)/(24EI)

= 5wL^4/(384EI) = 5*10*1000*10^4/(384*8*10^12)

= 1.627*10^-4 mm

the column BD resist this deflection

thus the the strain is =  1.627*10^-4/4000

= 4.069*10^-8

stress = young modulus*strain = 2000*4.069*10^-8 N/mm^2

= 8.138*10^-5

force = 8.138*10^-5*area of BD = 8.138*10^-5*50*50 = 0.203 N

same force is for spring = Kx

.203 = K*1.627*10^-4

K = 1250 KN/m

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