wid Se eve 
_ shear stress in lbs. per square inch. 
. in the text, and remembering that. the diagram in Fig. 203 
- determine the fraction which the total shear on the 
COMPOUND STRAINS AND STRESSES 153 
17. Two cross sections 1 inch apart of a rectangular beam 3 inches broad by 
8 inches deep are subjected to bending moments of 20 and 30 inch-tons respec- 
_ tively. Determine the maximum shear stress on the sections, and draw diagrams 
of shear stress and direct stress. [U.L.] 
18. A cantilever of mild steel 10 inches long, 2 inches deep, and 1} inches 
_ wide, carries a load of 1000 lbs, at its free end. Construct the curve which 
shows the intensity of the transverse shear stress at any point of the depth. 
Scales.—Linear, full size. Stress, 1 inch to 500 lbs. per square inch. 
19. A rolled steel joist has a total depth of 15 inches; the flanges are 6 
inches wide and 0°85 inch thick, and the web is 0°54 inch thick. The total trans- 
_ verse shear at a certain cross section is 30 tons. What is the maximum intensity 
of the shear stress in the cross section, and what multiple is it of the mean 
shear stress, assuming that the web takes the whole of the shear. Draw the 
diagram which shows the actual distribution of the shear stress in the cross section. 
f 
\ 
| 
} 
i 
(2) (6) (¢) (d) (e) (f) @) 
Fia. 213. 
20. Cross sections of various beams are shown in Fig. 213. If the shear 
stress at the neutral axis in each of these sections is 
6000 Ibs. per square inch, calculate for each the mean 
21. Referring to Fig. 203, page 150, and the dimensions he 
wn 
shows the variation of the intensity of the shear stress, s «3 
—_ 
Qa. 
section of the web is of the total shear on the whole . 
section. 6 
22. Deduce an expression for the intensity of shearing (Seas 
Stress at any place in a cross section of a beam. Draw 
to scale a di m showing the intensity of shear stress Fig. 214. 
throughout a cross section (Fig. 214), 2 feet from one 
‘toa a girder of 30 feet span, supported at the ends, and carrying a 
un y distributed load of 60 tons. The greatest moment of inertia is 3860, 
calculated from dimensions in inches. [U.L.] 
149. Bending Combined with Tension or Compression.—<A_ piece 
_ AB has an arm CD upon which a force P acts as shown in Fig. 215, the 
ee re 
Fiq. 215. 
line of action of P being parallel to the line YY, which is the edge view 
of the neutral surface of AB when considered as a beam subjected to 
bending, the plane of bending being the plane of the paper. 
Let XX be any cross section of AB, If forces P, and P, each equal 
