524
CHAPTER 8
Applications of Plane Stress
Combined Loadings
The problems for Section 8.5 are to be solved assuming that the structures behave linearly elastically and that the stresses caused by two or more loads may be superimposed to obtain the resulta
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
Deflections by Integration of the Shear Force and Load Equations
559
Deflections by Integration of the Shear Force and Load Equations
The beams described in the problems for Section 9.4 have constant flexural rigidity EI. Also, the origin of c
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
8
Applications of Plane Stress (Pressure Vessels, Beams, and Combined Loadings)
Spherical Pressure Vessels
When solving the problems for Section 8.2, assume that the given radius or diameter is an inside dimension and that all internal pressures are gage
466
CHAPTER 7
Analysis of Stress and Strain
Problem 7.5-8 A brass cube 50 mm on each edge is compressed in two perpendicular directions by forces P 175 kN (see figure). Calculate the change V in the volume of the cube and the strain energy U stored in the
452
CHAPTER 7
Analysis of Stress and Strain
Problem 7.4-7 An element in pure shear is subjected to stresses 3000 psi, as shown in the figure. xy Using Mohr's circle, determine (a) the stresses acting on an element oriented at a counterclockwise angle 70 f
SECTION 7.3
Principal Stresses and Maximum Shear Stresses
439
Problem 7.3-9 A shear wall in a reinforced concrete building is subjected to a vertical uniform load of intensity q and a horizontal force H, as shown in the first part of the figure. (The forc
7
Analysis of Stress and Strain
Plane Stress
Problem 7.2-1 An element in plane stress is subjected to stresses 6500 psi, y 1700 psi, and xy 2750 psi, as shown in the x figure. Determine the stresses acting on an element oriented at an angle 60 from the x
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 9.9
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
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
12
Review of Centroids and Moments of Inertia
Centroids of Plane Areas
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 and altitude h (see Ca
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 10.4
Method of Superposition
655
Problem 10.4-15 A temporary wood flume serving as a channel for irrigation water is shown in the figure. The vertical boards forming the sides of the flume are sunk in the ground, which provides a fixed support. Th
SECTION 10.4
Method of Superposition
643
Problem 10.4-2 The propped cantilever beam shown in the figure supports a uniform load of intensity q on the left-hand half of the beam. Find the reactions RA, RB, and MA, and then draw the shear-force and bending-
10
Statically Indeterminate Beams
Differential Equations of the Deflection Curve
The problems for Section 10.3 are to be solved by integrating the differential equations of the deflection curve. All beams have constant flexural rigidity EI. When drawing s
SECTION 6.8
Beams with Inclined Loads
403
Problem 6.8-3 A beam of wide-flange shape has the cross section shown in the figure. The dimensions are b 5.25 in., h 7.9 in., tw 0.25 in., and tf 0.4 in. The loads on the beam produce a shear force V 6.0 k at the
SECTION 6.4
Beams with Inclined Loads
391
Beams with Inclined Loads
When solving the problems for Section 6.4, be sure to draw a sketch of the cross section showing the orientation of the neutral axis and the locations of the points where the stresses are
160
CHAPTER 2
Axially Loaded Numbers
Stress Concentrations
The problems for Section 2.10 are to be solved by considering the stress-concentration factors and assuming linearly elastic behavior. Problem 2.10-1 The flat bars shown in parts (a) and (b) of th
144
CHAPTER 2
Axially Loaded Numbers
Problem 2.7-9 A slightly tapered bar AB of rectangular cross section and length L is acted upon by a force P (see figure). The width of the bar varies uniformly from b2 at end A to b1 at end B. The thickness t is const
134
CHAPTER 2
Axially Loaded Numbers
Problem 2.6-16 A prismatic bar is subjected to an axial force that produces a tensile stress 63 MPa and a shear stress 21 MPa on a certain inclined plane (see figure). Determine the stresses acting on all faces of a st
122
CHAPTER 2
Axially Loaded Numbers
Stresses on Inclined Sections
Problem 2.6-1 A steel bar of rectangular cross section (1.5 in. 2.0 in.) carries a tensile load P (see figure). The allowable stresses in tension and shear are 15,000 psi and 7,000 psi, re
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 1/8 in. Before they were loaded, all three wires had the s
80
CHAPTER 2
Axially Loaded Numbers
Problem 2.3-8 A bar ABC of length L consists of two parts of equal lengths but different diameters (see figure). Segment AB has diameter d1 100 mm and segment BC has diameter d2 60 mm. Both segments have length L/2 0.6
2
Axially Loaded Numbers
Changes in Lengths of Axially Loaded Members
Problem 2.2-1 The T-shaped arm ABC shown in the figure lies in a vertical plane and pivots about a horizontal pin at A. The arm has constant cross-sectional area and total weight W. A v
32
CHAPTER 1
Tension, Compression, and Shear
Problem 1.6-10 A flexible connection consisting of rubber pads (thickness t 9 mm) bonded to steel plates is shown in the figure. The pads are 160 mm long and 80 mm wide. (a) Find the average shear strain aver i