Handbook of Civil Engineering Calculations

Then^m = 2051/212.5 = 9.7 in (246 A mm). Since the area is symmetric with respect to the y axis, this is also a centroidal axis. ...

PRODUCT OF INERTIA OF AN AREA Calculate the product of inertia of the isosceles trapezoid in Fig. 14 with respect to the rectang ...

Compute the properties of the area with respect to the x' and y'axes Using the usual moment-of-inertia relations, we find Ix, = ...

STRESS CAUSED BYAN AXIAL LOAD A concentric load of 20,000 Ib (88,960 N) is applied to a hanger having a cross-sectional area of ...

FIGURE 16 Express the axial force P in each bar in terms of R 1 because both reactions are as- sumed to be directed toward the l ...

FIGURE 17 ^F 7 P 1 +P 2 + P 3 - 20,000 = O, or P 1 +P 2 + P 3 = 20,000, Eq. a; also, ^Mc = 16P 1 + 1OP 2 20,000(12) = O, or 16P ...

50,000 lb/in^2 (344,700 kPa). A load of 200 Ib (889.6 N) is suspended at the center of the cable. Determine the sag of the cable ...

(b) Displacement diagram FIGURE 19 (Fig. 196) line Ca parallel to member AC, with Ca = 0.0781 in (1.98 mm). Similarly, draw Cb p ...

STRESSES ON AN OBLIQUE PLANE A prism ABCD in Fig. 2Oa has the principal stresses of 6300- and 2400-lb/in^2 (43,438.5- and 16,548 ...

EVALUATION OF PRINCIPAL STRESSES The prism ABCD in Fig. 2 Ia is subjected to the normal and shearing stresses shown. Con- struct ...

Scale the diagram Scale OA and OB to obtain/max = 10,020 lb/in^2 (69,087.9 kPa);/min = 380 lb/in^2 (2620.1 kPa). Both stresses ...

Calculation Procedure: Compute the radial pressure caused by prestressing Use the relation;? = 2&D/{L>^2 [l/(taEa) + l/f ...

FIGURE 22 Thick-walled cylinder under internal and exter- nal pressure. Check the accuracy of the results Use the relation ^r 1 ...

Determine the compressive stress Use the relation s = EkLIL, where the symbols are as given earlier. Thus, s = 30(10^6 )(0.0823 ...

THERMAL EFFECTS IN COMPOSITE MEMBER HAVING ELEMENTS IN SERIES The aluminum and steel bars in Fig. 23 have cross-sectional areas ...

Calculation Procedure: Compute the temperature rise required Use the relation AT = AZ)/(c£>), where Ar = temperature rise re ...

Calculation Procedure: Determine the relationship between the torque in the shaft segments Since segments AB and BC (Fig. 24) a ...

Calculation Procedure: Determine the relationship between the torque in the shaft segments Since segments AB and BC (Fig. 24) a ...

SHEAR AND BENDING MOMENT IN A BEAM Construct the shear and bending-moment diagrams for the beam in Fig. 25. Indicate the value o ...

Determine the reaction at each support Take moments with respect to the other support. Thus ^Mn = 25RA - 6(21) - 20(20) - 45(7. ...