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 bar AB has a cross-sectional area of 225 mm2, determine (a) the factor of safety for bar AB, (b) the cross-sectional area of bar AC if it is to have the same factor of safety as bar AB.
Fig. P1.40 and P1.41
(a)
The factor of safety for bar AB.
Answer to Problem 41P
The factor of safety for bar 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 factor of safety for bar AB using the relation:
Here,
Modify Equation (5).
Substitute
Thus, the factor of safety for bar AB is
(b)
The cross sectional area of bar AC.
Answer to Problem 41P
The cross sectional area of bar AC is
Explanation of Solution
Calculation:
Show the expression factor of safety for bar AC using the relation:
Here,
Modify Equation (7).
Substitute
Thus, the cross sectional area of bar AC is
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Chapter 1 Solutions
EBK MECHANICS OF MATERIALS
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