Statics - Problem 6.15

  

From Chapter 6, Structural Analysis

In (Figure 1), a = 10 ft.$\mathrm{<span\; style="color:\; \#333333;\; font-family:\; arial;"> Members\; AB\; and\; BC </span>}$can each support a maximum compressive force of 950 lb, and members AD, DC, and BD can support a maximum tensile force of 

▼ PART A

Determine the greatest load  P the truss can support.

Express your answer to three significant figures and include the appropriate units.

 STEP 1  

Start by taking calculating the reaction forces about both support points.

Take moment abt. point A (which is a pin support.)

Solve for Cy;

Now, equate all vertical forces.

We have already solved for Cy, plug in its value;

 STEP 2 

Now, Create your FBD for the truss surrounding joint A.

Force AB is the force in member AB

& Force AD is the force in member AD.

Calculate the angles subtended by BAx & DAx.

BAx calculation:

*SOH CAH TOA

Use tangent for this angle calculation since we know the height (a) and the base (a).

DAx calculation:

*SOH CAH TOA

Use tangent for this angle calculation since we know the height (a/4) and the base (a).

 STEP 3 

Now, equate all horizontal forces.

Equate the forces along the vertical direction.

= 0.647P (tension)

 STEP 4 

Calculate the force in member AB:

= 0.943P (compression)

Due to symmetrical shape of ABD and BDC, the tensions in both members are equivalent.

= 0.647P

= 0.943P