Problem No.
TENSION CALCULATION IN AN L-SHAPED ROD AND CABLE SYSTEM
PROBLEM STATEMENT:
An L-shaped rod's position is controlled by a cable attached at point B, supporting a load
of P = 50 lb (see Figure 1). The task is to create a worksheet or spreadsheet to calculate the
tension (T) in the cable for values of θ ranging from 0 to 120° in 10° increments. Additionally,
using smaller increments, determine the maximum tension (T) and its corresponding value of θ.
RESULTS AND DISCUSSION:
Free Body Diagram:
Manual Solution:
Equation for ϕ:
AB sin θ−EF
tan ϕ=
AB cos θ+ AF
ϕ=tan −1 ( AB
AB cos θ+ AF )
sin θ−EF
Where, AB = 12, AF = 16, and EF = 8.
Equation for T:
∑ M A =0 ;−P ( ( AB+ BC ) sin θ+CD cos θ ) +T ¿
T =P ¿ ¿
Where; P = 50lb, AB = 12, BC = 15, and CD = 4
Equations above are then derived to be used in Excel Worksheet:
Here is a detailed step-by-step explanation of how the worksheet function:
1. Values of theta from 0-120 degrees with 10 increments are input in Angle (theta)
column.
2. Equations solved from the manual solution is made flexible and derived to excel
formulas to solve for angle phi and Tension T, the excel equation will be able to
solve for values for Phi and T even if the given P, AF, EF, AB, BC, and CD are
different from the given problem:
Angle Φ: =DEGREES(ATAN((E10*SIN(RADIANS(G7))-E9)/(E10*COS(RADIANS(G7))
+E8)))
Tension in Cable (T): =E7 * ((E10 + E11) * SIN(RADIANS(G7)) + E12 *
COS(RADIANS(G7))) / (E10 * SIN(RADIANS(G7 - H7)))
Similar Equations are also used to solve for the Maximum Tension in Cable
1. Values of theta from 50.40 – 50.47 degrees with 0.01 increments are input in Angle
(theta) column.
2. Equations solved from the manual solution is derived to solve for:
Angle Φ: =DEGREES(ATAN((E10*SIN(RADIANS(K11))-E9)/(E10*COS(RADIANS(K11))+E8)))
Tension in Cable (T): =E7 * ((E10 + E11) * SIN(RADIANS(K11)) + E12 *
COS(RADIANS(K11))) / (E10 * SIN(RADIANS(K11 - L11)))
From the Calculated Data:
(a) The Maximum Tension in Cable:
`
T = 132.227156
(b) Corresponding Value of θ:
θ = 50.45
PROBLEMS ENCOUNTERED:
The main problem faced during this task was formulating the Excel equations to
accurately represent the trigonometric relationships governing the tension (T) in the cable. The
challenge lay in translating mathematical expressions into a format suitable for Excel,
considering the need for flexibility in handling varying θ values. Special attention was given to
handling potential errors and ensuring the correct application of trigonometric functions.
To address these challenges, extensive testing of the Excel formulas was performed
with known values, and adjustments were made iteratively. Additionally, error-checking
mechanisms were implemented within the spreadsheet to enhance reliability.
REFERENCES:
1) Hibbeler, R. C. (2016). Engineering Mechanics: Statics. Pearson.
2) eHowTech. (2012, October 26). How to use TrIG functions in Excel : Excel Calculations
[Video]. YouTube. https://www.youtube.com/watch?v=Nlm2cl6OzaE
3) Vishap TVplus. (2019, March 19). Convert radians to degrees in Excel [Video].
YouTube. https://www.youtube.com/watch?v=51fPvZHz4CM
