Concept explainers
A plane truss is subjected to loads 2P and P at joints B and C, respectively, as shown in the figure part a. The truss bars are made of two L 102 X 76 X 6.4 steel angles (see Table F-5(b): cross-sectional area or the two angles, A = 2180 mm2, and figure part b) having an ultimate stress in tension equal to 390 MPa. The angles are connected to a 12-mm-thick gusset plate at C(figure part c) with 16-mm diameter rivets; assume each rivet transfers an equal share of the member force to the gusset plate. The ultimate stresses in shear and bearing for the rivet steel are 190 MPa and 550 MPa, respectively. Determine the allowable load Pallowif a safety factor of 2.5 is desired with respect to the ultimate load that can be carried. Consider tension in the bars, shear in the rivets, bearing between the rivets and gusset plate. Disregard friction between the plates the bars, and also bearing between the rivets and the and the weight of the truss itself.
The maximum load,
Answer to Problem 1.9.14P
The maximum load,
Explanation of Solution
Given:
Member forces from truss analysis:
Take moment about point A as follows:
Take summation of force in the vertical direction as follows:
Apply section method for the given truss as follows:
Take moment about point F as follows:
Take moment about point B as follows:
Take summation of force in the vertical direction as follows:
Change the direction of
Consider point D as an equilibrium point which is shown below:
Take summation of force in the vertical direction as follows:
Take summation of force in the horizontal direction as follows:
Consider point G as follows:
Take summation of force in the vertical direction as follows:
Thus, all the forces are:
The above force is less than the maximum force in a member. So, BC controls, since it has the largest member force for this loading.
The above area is less for one rivet in double shear.
Where,
N = number of rivets in a particular member
So, shear in rivets in CG&CD controls
Now,
Finally,
So, gusset will control over angles
So, shear in rivets controls:
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Chapter 1 Solutions
Mechanics of Materials (MindTap Course List)
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