The three-box turns ABC shown in the figure part a has a span L= 3 m and is cons

Question

The three-box turns ABC shown in the figure part a has a span L= 3 m and is constructed of steel pipes having cross-sectional area A = 3900 mm2 and modulus of clasticity E = 200GPa. Identical loads P act both vertically and horizontally at joint C as shown If P = 475 kN, what is the horizontal displacement of joint B? What is the maximum permission load value P max if the displacement of joint B is limited B is limited to 1.5 mm? Repeat parts and if the plane truss is replaced by a space truss (see figure part b)

Explanation / Answer

E=200 Gpa

E=(F/A)/(δl/l)

(a)

as 2 forces are at right angles

=> effective force is (F*√2) in the direction of CB
Effective force= 475000*√2=671751.4 
200x103= (671751.4 /3900)/strain

strain =8.61x10-4

δl/l =8.61x10-4

δl/3 =8.61x10-4

δl =2.58 mm

(b)

δl = 1.5mm

δl/l = 5x10-4

Stress = E x Strain

Stress = 200x103 x 5X10-4

Stress = 1000
F/3900 = 1000

F= 3900000 N

p =F/√2

P= 2750Kn

(C)
space truss image is not clear..(Fig b)

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