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
SECTION 5.12
Beams with Axial Loads
363
Problem 5.12-10 A flying buttress transmits a load P 25 kN, acting at an angle of 60 to the horizontal, to the top of a vertical buttress AB (see figure). The vertical buttress has height h 5.0 m and rectangular cro
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
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
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
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
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
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 9.5
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
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 9.11
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
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 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
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
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 11.5
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
304
CHAPTER 5
Stresses in Beams (Basic Topics)
Design of Beams
Problem 5.6-1 The cross section of a narrow-gage railway bridge is shown in part (a) of the figure. The bridge is constructed with longitudinal steel girders that support the wood cross ties.
350
CHAPTER 5
Stresses in Beams
Built-Up Beams
Problem 5.11-1 A prefabricated wood I-beam serving as a floor joist has the cross section shown in the figure. The allowable load in shear for the glued joints between the web and the flanges is 65 lb/in. in
122
CHAPTER 2
Axially Loaded Members
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 Members
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
2
Axially Loaded Members
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
80
CHAPTER 2
Axially Loaded Members
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
1
Tension, Compression, and Shear
Normal Stress and Strain
Problem 1.2-1 A solid circular post ABC (see figure) supports a load P1 2500 lb acting at the top. A second load P2 is uniformly distributed around the shelf at B. The diameters of the upper and l
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
134
CHAPTER 2
Axially Loaded Members
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
160
CHAPTER 2
Axially Loaded Members
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
236
CHAPTER 3
Torsion
Strain Energy in Torsion
Problem 3.9-1 A solid circular bar of steel (G 11.4 106 psi) with length L 30 in. and diameter d 1.75 in. is subjected to pure torsion by torques T acting at the ends (see figure). (a) Calculate the amount of
3
Torsion
Torsional Deformations
Problem 3.2-1 A copper rod of length L 18.0 in. is to be twisted by torques T (see figure) until the angle of rotation between the ends of the rod is 3.0. If the allowable shear strain in the copper is 0.0006 rad, what is
144
CHAPTER 2
Axially Loaded Members
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