The side girder shown in the photo supports the boat and deck. An idealized model of this girder is shown in Fig. 2–31a, where it can be assumed A is a roller and B is a pin. Using a local code the anticipated deck loading transmitted to the girder is 6 kN m. Wind exerts a resultant horizontal forc

Question

The side girder shown in the photo supports the boat and deck. An idealized model of this girder is shown in Fig. [latex] 2-31 (\mathrm{a})[/latex], where it can be assumed [latex]A[/latex] is a roller and [latex]B[/latex] is a pin. Using a local code the anticipated deck loading transmitted to the girder is [latex]6 \mathrm{kN} / \mathrm{m}[/latex]. Wind exerts a resultant horizontal force of [latex]4 \mathrm{kN}[/latex] as shown, and the mass of the boat that is supported by the girder is [latex]23 \mathrm{Mg}[/latex]. The boat's mass center is at [latex]G[/latex]. Determine the reactions at the supports.

Accepted Answer

Free-Body Diagram. Here we will consider the boat and girder as a single system, Fig. 2-31b. As shown, the distributed loading has been replaced by its resultant.

Equations of Equilibrium. Applying Eqs. 2-2 in sequence, using previously calculated results, we have

[latex]\begin{aligned} \Sigma F_{x} &=0 \ \Sigma F_{y} &=0 \ \Sigma M_{O} &=0 \end{aligned}[/latex] (2-2)

[latex]\begin{array}{cc}\stackrel{+}{ ightarrow} \Sigma F_{x}=0 ; & 4-B_{x}=0 \ & B_{x}=4 \mathrm{kN} \ \curvearrowleft + \Sigma M_{B}=0 ; & 22.8(1.90)-A_{y}(2)+225.6(5.40)-4(0.30)=0 \ & A_{y}=630.2 \mathrm{kN}=630 \mathrm{kN} \ +\uparrow \Sigma F_{y}=0 ; & 630.2-B_{y}-22.8-225.6=0 \ & B_{y}=382 \mathrm{kN}\end{array}[/latex]

Note: If the girder alone had been considered for this analysis then the normal forces at the shoes [latex]C[/latex] and [latex]D[/latex] would have to first be calculated using a free-body diagram of the boat. (These forces exist if the cable pulls the boat snug against them.) Equal but opposite normal forces along with the cable force at [latex]E[/latex] would then act on the girder when its free-body diagram is considered. The same results would have been obtained; however, by considering the boat-girder system, these normal forces and the cable force become internal and do not have to be considered.

Question 2.11: The side girder shown in the photo supports the boat and dec...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions