QUESTIONS AND PROBLEMS. CHAPTER VI. 



125 



when the span is 36 ft., PI =80, P 2 = 120, P 3 = 60, P 4 = 40, 

 P 5 = 112, ai = 5 ft., a 2 = ll ft., a 3 = 20 ft., a 4 = 24 ft., and 

 a 5 = 32 ft. Find the maximum moment. Where is the moment 

 a minimum? 



32. Illustrate a case in which the shear is uniform over a 

 part of a beam, along which the increase of the moment is 

 uniform. 



33. Construct a shear diagram for problem 31, and find 

 the area of that part to the left of the section of maximum 

 moment. 



34. What is the unit shearing stress at the neutral axis, in 

 a vertical section of a timber beam 12"xl2", if the total shear at 

 the section is 43200 Ibs.? What is the unit horizontal shearing 

 stress at the same point? 



35. At what points in a circular cross section is the shear- 

 ing stress zero? At what points is it a maximum? In what 

 direction does the shearing stress at the circumference act? 



36. At what points in a beam is the bending stress a prin- 

 cipal stress? Can a shearing stress be a principal stress in a 

 beam? At what points are the resultants of shearing stresses 

 principal stresses? 



37. When does the shearing stress in a beam become more 

 important than the bending stress? 



38. What is the direction of lines of maximum and mini- 

 mum shear at the neutral plane? 



39. What are the principal stresses in the web of an I 

 beam at a point where the bending stress is 11000 Ibs. per sq. 

 in., and the shearing stress 2800 Ibs. per sq. in.? 



40. In the above problem, what is the equivalent simple 

 stress according to equation (31)? 



41. What is the function of the web in a plate girder? Of 

 the flanges? 



42. Do the assumptions made in calculating stresses in 

 plate girders give results too large or too small? What is the 

 value of these assumptions? 



43. How is the effective depth of a girder determined? 



44. What is the effective depth of a girder having a 56"x 

 5-16" web and 2 angles 6"x6"xf" in each flange, the extreme 

 Jepth outside of flanges being 56 J"? What is the equivalent 

 flange stress if the moment is 480000 ft. Ibs.? What is the 



