Using the property indicated in Prob. 7.124, determine the curve assumed by a cable of span L and sag h carrying a distributed load w = w0 cos (πx/L), where x is measured from mid-span. Also determine the maximum and minimum values of the tension in the cable.
PROBLEM 7.124 Show that the curve assumed by a cable that carries a distributed load w(x) is defined by the differential equation d2y/dx2 = w(x)/T0, where T0 is the tension at the lowest point.
The expression for the curve made by the cable, maximum and minimum values of the tension in the cable.
Answer to Problem 7.125P
The curve represented by the cable is
Explanation of Solution
The figure 1 below shows the cable and which makes the curve due the load w.
Write the expression for the load distributed.
Refer the problem 77268-7.4-7.124P and writhe the differential equation for the curve.
Write the expression for the differential equation for the curve.
Substitute
Integrate both side of the above equation and apply the condition
Integrate the above equation and apply the condition
Here C is the integration constant.
Apply the condition
Substitute
At
Substitute
The value of y at
Rewrite the above equation in terms of h.
Here
Therefore the minimum tension on the cable is
To find the maximum tension on the cable the slope of the above equation for y at
Here
Substitute
Rewrite the above equation in terms of
Write the expression to calculate the maximum tension on the cable.
Here
Substitute
Conclusion:
Thus, the curve represented by the cable is
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Chapter 7 Solutions
VECTOR MECH....F/ENGNRS-STATICS -CONNECT
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