In the next sections of this book numerous illustrative examples are given in detail in order to show the application of the various methods and principles. Accompanying these are samples for practice which will aid the reader in fixing the principles in mind.

In the following pages are given a large number of test questions and problems which afford a valuable means of testing the reader's knowledge of the subjects treated. They will be found excellent practice for those preparing for Civil Service Examinations. In some cases numerical answers are given as a further aid in this work.

## Review Questions On The Subject Of Strength Of Materials. Part I

1. When a ¾-inch round rod sustains a pull of 10,000 pounds, what is the value of the unit-tensile stress in the rod?

2. What do you understand by Hooke's Law?

3. What are the dimensions of a square white pine post, needed to support a steady load of 6,500 pounds with a factor of safety of 8?

4. How large a force is required to punch a 1-inch hole through a ¾-inch plate of wrought iron, if the ultimate shearing strength of the material is 40,000 pounds per square inch ?

5. Compare the ultimate strengths of wood along and across the grain; also the ultimate tensile and compressive strengths of cast iron.

6. Make a sketch of a beam 20 feet long resting on end supports, and represent loads of 6,000, 3,000, 1,000, and 4,000 pounds at points 2, 5, 11, and 16 feet from the left end, respectively. What is the value and sign of the moment of each of these loads about the middle of the beam? Also about the left end?

7. A beam 15 feet long is supported at two points, 2 feet from the right end, and 3 feet from the left end. If the beam sustains a uniform load of 400 pounds per foot, what are the values of the reactions?

8. Compute the values of the external shear and bending moment for the loaded beam described in question 6, at sections 1 4, 10, and 15 feet from the left end.

9. Draw shear and moment diagrams to scale for the beam described in question7.

10. Suppose a T-bar 2 inches deep, has a flange 3 inches wide, and is ¼ inch thick throughout. Locate the center of gravity by computation.

11. Cut a piece of stiff paper to the dimensions given in the preceding question, locate its center of gravity by balancing, and state its distance from the base as you find it by this method.

12. Draw a 1-inch, a 2-inch, and a 3-inch square touching each other, so that the 2-inch rests on the 3-inch square, and the 1-inch on the 2-inch square, three of the sides being in the same line. How far from the bottom and the side is the center of gravity of the three squares ?

13. Compute the moment of inertia of a rectangle 2 X 16 inches with respect to its long side.

14. A square stick of red oak timber is to carry a compressive load of 15,000 pounds. What should be its size in order that the unit-stress may be one-half the ultimate strength along the grain ?

15. A pressed brick 2 X 4 X 8½ inches weighs about 5½ pounds. What will be the height of a pile of brick, so that the unit-stress on the lower brick shall be one-half its ultimate strength ? Use 8,000 pounds as the ultimate strength of the pressed brick.

16. From the diagram shown on page 11, determine the elastic limit of wrought iron, in tension.

17. A wrought-iron rod 2 inches in diameter sustains a load of 50,000 pounds. What is its working stress ? If its ultimate strength is 60,000 pounds per square inch, find its factor of safety.

18. A wrought-iron bar 3 inches in diameter ruptures under a tension of 200,000 pounds. What is its ultimate strength?

19. Find the diameter of a cast-iron bar designed to carry a tension of 250,000 pounds with a factor of safety of 6. If the bar were of wrought iron, what would be its diameter?

20. A wrought-iron bar is to be under a stress of 50,000 pounds. Find its diameter when it is to be used in a building; also when it is to be used in a bridge.

21. Find the greatest steady load a short timber post can sustain with safety, when it is 8 X 8 inches in cross-section and its ultimate compressive strength is 10,000 pounds per square inch.

22. A wrought-iron bolt 1½ inches in diameter has a head

1¼ inches long. If a tension of 15,000 pounds is applied to the bolt, find the tensile unit-stress and the factor of safety for tension. Also find the unit-stress tending to shear off the head of the bolt, and the factor of safety against shear.

23. Find the reactions due to the loads in Fig. 9, when the beam is supported at its ends, and the loads are 2,000, 5,000, and 3,000 pounds respectively.

24. Compute the shear for sections one foot apart in the beam represented in Fig. 9, taking into consideration the weight of the beam, 500 pounds, and a distributed load of 400 pounds per foot, in addition to the loads as shown in Fig. 9.

25. Construct the shear diagram for the cantilever beam loaded as shown in Fig. 15, when the weight of the beam is 600 pounds, and the beam sustains a uniform load of 300 pounds per foot.

26. A cantilever beam has a load of 800 pounds at its end and is also uniformly loaded with 125 pounds per linear foot; its length is 5 feet. Compute the bending moments for five sections one foot apart, and construct the diagram of bending moments.

27. A deck beam used in building has a rectangular flange 3 inches X ½ inch; a rectangular web 4 inches X ½ inch; and an elliptical head which is l½ inches in depth, and whose area is 2.6 square inches. Find the distance of the center of gravity from the top of the head.

28. Compute the moment of inertia of a steel I-beam weighing 60 pounds per linear foot, it being 20 inches deep, with flange 5 inches wide, and mean thickness ⅜ inch. The web is ¾ inch thick and has a moment of inertia of 446 inches.

## Review Questions On The Subject Of Strength Of Materials. Part II

1. A cantilever beam 6 feet in length projects from a wall and sustains an end load of 300 pounds. The cross-section being as in Fig.' 38, find the greatest tensile and compressive unit-stresses, and state where they occur.

2. An I-beam weighing 30 pounds per foot, rests on end supports 25 feet apart. Its section modulus is 20.4 inches3, and its working strength 16,000 pounds per square inch. Calculate weight of the beam.

3. A wooden beam 15 feet long, 4 X 14 inches in cross-eection sustains a load of 4,000 pounds 5 feet from one end, and 5,000 pounds at the middle. Compute the greatest unit shearing stress.

4. What do you know about radius of gyration? Give an example.

5. Find the factor of safety of a 24-inch 80-pound steel I-beam 15 feet long, used as a flat-ended column to sustain a load of 150,000 pounds. Note. - Use "Rarkine's Formula."

6. A steel Z-bar is 20 feet long and has square ends; the least radius of gyration of its cross-section is 3.1 inches, and its area of cross-section is 24.5 square inches. Calculate the safe load with a factor of safety of 6. Note. Use "Rankine's Formula."

7. Make sketches of the following :

Lap joint single-riveted;

" " double-riveted; Butt " single-riveted;

" " double-riveted.

8. The ends of a cast-iron rod 2 inches in diameter are secured to two heavy bodies which are to be drawn together, the temperature of the rod being 300 degrees when fastened to the objects. A fall of 125 degrees has no effect on the objects. Compute the temperature stress, and state the pull exerted by the rod on each object.

9. Two half-inch plates 6 inches wide are connected by a lap joint with three ¾-inch rivets in a row. What is the safe strength of the joint?

10. A timber beam 6 X 14 inches and 20 feet long rests on end supports and sustains two loads of 3,000 pounds each five feet from the ends. Compute the values of the greatest unit-tension, compression, and shear in the beam.

11. A 20-pound 7-inch I-beam 12 feet long is used as a cantilever beam supported in the middle. If its working strength is 10,000 pounds per square inch, find the greatest safe load that can be hung at each end considering the weight of the beam.

12. Compute the safe middle load for a 25-pound 10-inch I-beam 20 feet long, resting on end supports, if its working strength is 16,000 pounds per square inch. Consider.the weight of the beam.

13. The width of the flanges of an 18-pound 8-inch I-beam is 4 inches. Compare the strengths of such a beam when used (1) with its web vertical (Fig. 24), and (2) when its web is horizontal.

11. A bar of steel 1x6 inches in section and 24 feet long is used as a beam on end supports, its load being 2,000 pounds uniformly distributed, and it also sustains end pulls of 20,000 pounds. Compute the greatest unit-tensile and compressive stresses in the bar by approximate methods. (See Art. 74.)

15. A timber beam 0 X 12 inches and 20 feet long on end supports bears a Uniform load of 3,000 pounds, and end pushes of L5,000 pounds. Compute the greatest unit-tensile and compressive stresses in the timber by approximate methods. (See Art. 75.)

16. Answer the two preceding questions by the exact methods of Art. 76.

17. Two I-beams (instead of channels) are fastened together as represented in Fig. 46, b, to make a column. They are 40-pound 12-inch beams, the plates are ⅝ inch thick and 16 inches wide; and from center to center of the webs of the beams is 10 inches. Compute the radii of gyration of the column section with respect to two axes through the center of gravity parallel and perpendicular to the webs.

18. Compute the safe loads for two white pine columns 16 x 16 and 8x8 inches, each 14 feet long, using a factor of safety of 6.

19. What size of white oak column 16 feet long is needed to carry a load of 10,000 pounds with a factor of safety of 5? What size of steel I-beam will carry the same load if the ends of the column are flat? Note. - Solve for r, and use table C.

20. Compute the size of a circular, hollow, cast-iron column to carry a load of 150,000 pounds with a factor of safety of 10, its length being 18 feet and its ends flat. Note. Use "Rankine's Formula," and try an outside diameter of 10 inches.

21. If a solid shaft 4 inches in diameter is subjected to a twisting moment of 1,000 foot-pounds, compute the greatest unit-shearing stress in the shaft.

22. Compute the number of horse-power which a steel shaft 6 inches in diameter can safely transmit at 200 revolutions per minute, if its working strength in shear is 10,000 pounds per square inch.

23. What size of circular shaft is needed to transmit 1,600 horse-power at 100 revolutions per minute, if the working strength of the material in shear is 12,000 pounds per square inch?

24. How much will a round steel rod, 1 inch in diameter and 20 feet long, elongate under a pull of 10,000 pounds?

25. Compute the deflection of a 15-pound 7-inch I-beam 10 feet long, when resting on end supports and sustaining a uniform load of 5,000 pounds.

26. Two bars of the same size, one of wrought iron and one of cast iron, rest on end supports and sustain equal central loads which are "safe" in each. case. Which beam deflects most, and what is the ratio of the deflection?

27. A bar of wrought iron 10 feet long will shorten how many inches during a drop of 40 degrees Fahrenheit in its temperature?

28. If the bar of the preceding question is restrained and prevented from shortening, what unit-stress is produced in it by the drop in temperature?