SECTION 12.6
Polar Moments of Inertia
15
Polar Moments of Inertia
Problem 12.6-1 Determine the polar moment of inertia IP of an isosceles triangle of base b and altitude h with respect to its apex (see Case 5, Appendix D) Solution 12.6-1 Polar moment of i

12
Review of Centroids and Moments of Inertia
Differential Equations of the Deflection Curve
The problems for Section 12.2 are to be solved by integration.
Problem 12.2-1 Determine the distances x and y to the centroid C of a right
triangle having base b

SECTION 11.9
Design Formulas for Columns
711
Problem 11.9-9 Determine the allowable axial load Pallow for a steel pipe column that is fixed at the base and free at the top (see figure) for each of the following lengths: L 6 ft, 9 ft, 12 ft, and 15 ft. The

SECTION 11.5
Columns with Eccentric Axial Loads
697
Problem 11.5-13 A frame ABCD is constructed of steel wide-flange members (W 8 21; E 30 10 6 psi) and subjected to triangularly distributed loads of maximum intensity q0 acting along the vertical members

682
CHAPTER 11
Columns
Columns with Other Support Conditions
The problems for Section 11.4 are to be solved using the assumptions of ideal, slender, prismatic, linearly elastic columns (Euler buckling). Buckling occurs in the plane of the figure unless st

11 #
Columns Chapter Title
Idealized Buckling Models
Problem 11.2-1 through 11.2-4 The figure shows an idealized structure consisting of one or more rigid bars with pinned connections and linearly elastic springs. Rotational stiffness is denoted R and tra

SECTION 9.11
Representation of Loads on Beams by Discontinuity Functions
615
Representation of Loads on Beams by Discontinuity Functions
Problem 9.11-1 through 9.11-12 A beam and its loading are shown in the figure. Using discontinuity functions, write th

SECTION 9.9
Castigliano's Theorem
601
Castigliano's Theorem
The beams described in the problems for Section 9.9 have constant flexural rigidity EI. Problem 9.9-1 A simple beam AB of length L is loaded at the left-hand end by a couple of moment M0 (see fig

588
CHAPTER 9
Deflections of Beams
Nonprismatic Beams
Problem 9.7-1 The cantilever beam ACB shown in the figure has moments of inertia I2 and I1 in parts AC and CB, respectively. (a) Using the method of superposition, determine the deflection B at the fre

SECTION 9.5
Method of Superposition
571
q0
Problem 9.5-11 Determine the angle of rotation B and deflection B at the free end of a cantilever beam AB supporting a parabolic load defined by the equation q q0 x 2/L2 (see figure).
y A
B
x
L
Solution 9.5-11
Ca

SECTION 9.4
Differential Equations of the Deflection Curve
559
Differential Equations of the Deflection Curve
The beams described in the problems for Section 9.4 have constant flexural rigidity EI. Also, the origin of coordinates is at the left-hand end o

9
Deflections of Beams
Differential Equations of the Deflection Curve
The beams described in the problems for Section 9.2 have constant flexural rigidity EI. Problem 9.2-1 The deflection curve for a simple beam AB (see figure) is given by the following eq

106
CHAPTER 2
Axially Loaded Numbers
Problem 2.5-3 A rigid bar of weight W 750 lb hangs from three equally spaced wires, two of steel and one of aluminum (see figure). The diameter of the wires is 18 in. Before they were loaded, all three wires had the sa