1- Tension force of BC (TBC) is dependent on tension force of AB (TAB) by ? 2- The tension force of AB (TAB) is related to w by ? 3- The tension force of BC (TBC) is related to w by ? 4- The allowable stress (σ all.) is ? 5- The maximum safe value of w is ?

1- Tension force of BC (TBC) is dependent on tension force of AB (TAB) by ? 2- The tension force of AB (TAB) is related to w by ? 3- The tension force of BC (TBC) is related to w by ? 4- The allowable stress (σ all.) is ? 5- The maximum safe value of w is ?

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Question

1- Tension force of BC (TBC) is dependent on tension force of AB (TAB) by ?

2- The tension force of AB (TAB) is related to w by ?

3- The tension force of BC (TBC) is related to w by ?

4- The allowable stress (σ all.) is ?

5- The maximum safe value of w is ?

Expert Solution

Part-1 Step-1

Given:

Dimensions as given in figure.

Step 2

The equation for triangle AEB can be given by,

$\begin{array}{rcl} \tan (θ_{1}) & = & \frac{A E}{E B} \\ θ_{1} & = & \tan^{- 1} (\frac{1}{2}) \\ θ_{1} & = & 26 . 56^{o} \end{array}$

The equation for triangle BDC can be given by,

$\begin{array}{rcl} \tan (θ_{2}) & = & \frac{C D}{D B} \\ θ_{2} & = & \tan^{- 1} (\frac{6}{6}) \\ θ_{2} & = & 45^{o} \end{array}$

Step 3

Now resolving the tensions T_AB and T_BC in vertical and horizontal directions.

Step 4

The equation for net horizontal forces can be given by,

$\begin{array}{rcl} \sum_{}^{} F_{x} & = & 0 \\ T_{B C} \sin θ_{2} - T_{A B} \sin θ_{1} & = & 0 \\ T_{B C} \sin θ_{2} & = & T_{A B} \sin θ_{1} \end{array}$