Concept explainers
Members AB and BC of the truss shown are made of the same alloy. It is known that a 20-mm-square bar of the same alloy was tested to failure and that an ultimate load of 120 kN was recorded. If a factor of safety of 3.2 is to be achieved for both bars, determine the required cross-sectional area of (a) bar AB, (b) bar AC.
Fig. P1.40 and P1.41
(a)
The required cross sectional area of member AB.
Answer to Problem 40P
The required cross sectional area of AB is
Explanation of Solution
Given information:
The ultimate load
The factor of safety F.S is
The area (a) of square cross section is
Calculation:
Refer to Figure P1.40 in the text book.
Find the length of member
Sketch the free body diagram of truss as shown in Figure 1.
Here,
Refer to Figure 1.
Calculate the horizontal reaction A by using equilibrium Equation as follows:
Calculate the vertical reaction
Sketch the free body diagram of joint A as shown in Figure 2.
Refer to Figure P1.40 in the text book.
Refer to Figure 2.
Substitute
Refer to Figure 2.
Substitute
Find the area of test bar (A) using the relation:
Substitute
Find the ultimate load for the material using the formula:
Here,
Substitute
Determine the area of member
Show the expression of factor of safety as follows:
Here,
Modify Equation (5).
Substitute 3.2 for F.S,
Thus, the required cross sectional area of AB is
(b)
The required cross sectional area of AC.
Answer to Problem 40P
The required cross sectional area of AC is
Explanation of Solution
Determine the area of member
Show the expression of factor of safety as follows:
Modify Equation (7).
Substitute 3.2 for F.S,
Thus, the required cross sectional area of AC is
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Chapter 1 Solutions
Mechanics of Materials, 7th Edition
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