III An old single-leaf drawbridge is made ofa thin rectangular board of mass M,width a (into the page) and length bwhich can pivot at one end. When it is notin use, the span of the bridge is held at a60° angle from the horizontal direction.boardcables60°30°The two ideal cables that hold it at itsfarther end are anchored to the ground sothat they form a 30° angle with thehorizontal direction, as shown in Fig. 3.The accelerationhingecanaldueto gravity hasmagnitude g.Figure 3a- Draw the free body diagram of the rectangular board. Each force should be properlylabeled and represented where it applies.b- Set up all the detailed scalar equations (not the general version) expressing the staticequilibrium of the drawbridge. c- Determine the magnitude T of the tension force exerted by each of the two cables onthe board.d- Determine the magnitude Fr of the hinge force exerted on the board and the angle Onthat the force forms with respect to the horizontal direction.

Question is based on the old single - leaf draw bridge hinged at one end . Angle cable and bridge…

An old single-leaf drawbridge is made of a thin rectangular board of mass M, width a (into the page) and length b- which can pivot at one end. When it is not in use, the span of the bridge is held at a 60° angle from the horizontal direction. The two ideal cables that hold it at its farther end are anchored to the ground so that they form a 30° angle with the horizontal direction, as shown in Fig. 3. The acceleration due to gravity has magnitude g

An old single-leaf drawbridge is made of a thin rectangular board of mass M, width a (into the page) and length b- which can pivot at one end. When it is not in use, the span of the bridge is held at a 60° angle from the horizontal direction. The two ideal cables that hold it at its farther end are anchored to the ground so that they form a 30° angle with the horizontal direction, as shown in Fig. 3. The acceleration due to gravity has magnitude g

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

III

An old single-leaf drawbridge is made of
a thin rectangular board of mass M,
width a (into the page) and length b
which can pivot at one end. When it is not
in use, the span of the bridge is held at a
60° angle from the horizontal direction.
board
cables
60°
30°
The two ideal cables that hold it at its
farther end are anchored to the ground so
that they form a 30° angle with the
horizontal direction, as shown in Fig. 3.
The acceleration
hinge
canal
due
to gravity has
magnitude g.
Figure 3
a- Draw the free body diagram of the rectangular board. Each force should be properly
labeled and represented where it applies.
b- Set up all the detailed scalar equations (not the general version) expressing the static
equilibrium of the drawbridge.

c- Determine the magnitude T of the tension force exerted by each of the two cables on
the board.
d- Determine the magnitude Fr of the hinge force exerted on the board and the angle On
that the force forms with respect to the horizontal direction.

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Step 1 Introduction

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Step 2 Data Given

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Step 3 Tension on the cable

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Step 4 Static equilibrium equation

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Step 5 Calculation of force on hinge

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Step 6 Conclusion

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