Question

The cable shown in the following figure is subjected to the uniform loading. If the slope of the cable at point is zero, determine: 1- The equation of the curve, and [ABET: 1.1- 3 Marks] 2- Determine the maximum and minimum tension in the cable. [ABET: 1.3-4 Marks 10 m 10 m 16 kN/m

Answer 1

a)

Equation of cable is given as

v-4ha(L- L2

where y= dip at a point

h = maximum dip

L= length of cable

here L= 20m and h= 2 m , thereofore we get

| 4*2* _T(20 - c} c(20 - ar) 50 20一二

$y=\frac{x(20-x)}{50}$

Horizontal reaction at support Aor B

$H_A=H_B=H=\frac{wL^2}{8h}$

$here\,w=16\,KN/m$

$H=\frac{16*20^2}{8*2}=400KN$

vertical reaction at support A or B

$V_A=V_B=V=\frac{wL}{2}$

$V=\frac{16*20}{2}=160 KN$

$Maximum\,tension \,in\,cable\,(T_{max})=\sqrt{V^2+H^2}$

$(T_{max})\,occurs\,at\,support\,A\,or\,B$

$(T_{max})=\sqrt{160^2+400^2}=80\sqrt{29}\,KN$

$(T_{min})\,occurs\,at\.mid\,point\,O$

$(T_{max})=80\sqrt{29}KN\,\,\,\,\,\,\,\,\,\,\,\,\,\,at\,A\,or\,B$

for any query you can ask me in the comment section. i wil be happy to help you

and please dont forget to like