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
Want to see more full solutions like this?
Chapter 1 Solutions
Mechanics of Materials, 7th Edition
- ! Required information Each of the five struts shown consists of a solid steel rod with E= 200 GPa. Given: Po = 7.2 kN 900 mm Po (1) Po (2) Po (3) (5) Knowing that the strut of Fig. (1) is of a 20-mm diameter, determine the factor of safety with respect to buckling for the loading shown. (Round the final answer to two decimal places. You must provide an answer before moving the the next part.) The factor of safety isarrow_forward5.arrow_forwardTwo portions of member AB are glued together along a plane forming an angle with the horizontal. The ultimate stress for the glued joint is 3.3 ksi in tension and 2.2 ksi in shear. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 2.0 in. B 2.4 kips 1.25 in. Determine the value of 0 for which the factor of safety of the member is maximum. (Hint: Equate the expressions obtained for the factors of safety with respect to the normal and shearing stresses.)arrow_forward
- A load P is supported as shown by a steel pin that has been inserted in a short wooden member hanging from the ceiling. The ultimate strength of the wood used is 60 MPa in tension and 7.5 MPa in shear,while the ultimate strength of the steel is 145 MPa in shear. Knowing that b = 40 mm, c = 55 mm, and d = 12 mm, determine the load P if an overall factor of safety of 3.2 is desired.arrow_forward1.18 Determine the smallest safe cross-sectional areas of members CD, GD, and GF for the truss shown. The working stresses are 140 MPa in tension and 100 MPa in compression. (The working stress in compression is smaller to reduce the danger of buckling.) ARE 6m 4m 4 m E 6 m H 6m 6 m F 6m 140 kN 140 kN FIG. P1.18arrow_forwardThe steel frame (E = 200 GPa) shown has a diagonal brace BD with an area of 1920 mm2. Determine the largest allowable load P if the change in length of member BD is not to exceed 1.9 mm.The largest allowable load P isarrow_forward
- A pin-connected structure is supported and loaded as shown. Member ABCD is rigid and is horizontal before the load P is applied. Bars (1) and (2) are both made from steel [E = 30,000 ksi] and both have a cross-sectional area of 1.25 in.?. If the normal stress in bar (1) must be limited to 23 ksi, determine the maximum load P that may be applied to the rigid bar. 120 in. 80 in. (2) (1) B C 54 in. 54 in. 24 in. O 40.7 kips O 60.3 kips 32.2 kips 43.1 kipsarrow_forwardA pin-connected structure is supported and loaded as shown. Member ABCD is rigid and is horizontal before the load P is applied. Bars (1) and (2) are both made from steel [E = 30,000 ksi] and both have a cross-sectional area of 1.25 in.?. If the normal stress in bar (1) must be limited to 31 ksi, determine the maximum load P that may be applied to the rigid bar. 120 in. 80 in. (2) (1) B D 54 in. 54 in. 24 in. Parrow_forwardA steel loop ABCD of length 5 ft and of 3838 -in. diameter is placed as shown around a 1-in.-diameter aluminum rod AC. Cables BE and DF, each of 1212 -in. diameter, are used to apply the load Q. Knowing that the ultimate strength of the steel used for the loop and the cables is 75 ksi, and that the ultimate strength of the aluminum used for the rod is 45 ksi, determine the largest load Q that can be applied if an overall factor of safety of 3 is desired. The largest load Q that can be applied is kips.arrow_forward
- In the truss shown, members AC and AD consist of rods made of the same metal alloy. Knowing that AC is of 1-in. diameter and that the ultimate load for that rod is 75 kips, determine (a) the factor of safety for AC, (b) the required diameter of AD if it is desired that both rods have the same factor of safety.arrow_forwardplease answer number 4.Mech 222- mechanics of deformable bodies:please give detailed solutions and correct answers.i will report to bartleby those tutors who will give incorrect answers.arrow_forwardA square aluminum bar should not stretch more than 1.4 mm when it is subjected to a tensile load.Knowing that E = 70 GPa and that the allowable tensile strength is 120 MPa, determine the maximumallowable length.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY