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 (
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
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 h
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
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 follow
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
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 strai
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
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
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
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 ori
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
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
Solut
4
Shear Forces and Bending Moments
Shear Forces and Bending Moments
Problem 4.3-1 Calculate the shear force V and bending moment M at a cross section just to the left of the 1600-lb load acting on the simple beam AB shown in the figure.
A 30 in.
80
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, wh
204
CHAPTER 3
Torsion
Problem 3.4-9 A tapered bar AB of solid circular cross section is twisted by torques T 36,000 lb-in. (see figure). The diameter of the bar varies linearly from dA at the left-hand end to dB at the right-hand end. The bar has
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 a
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. (
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
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 cros
SECTION 5.7
Nonprismatic Beams
321
Nonprismatic Beams
Problem 5.7-1 A tapered cantilever beam AB of length L has square cross sections and supports a concentrated load P at the free end (see figure on the next page). The width and height of the be
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 an
5
Stresses in Beams (Basic Topics)
Longitudinal Strains in Beams
Problem 5.4-1 Determine the maximum normal strain max produced in a steel wire of diameter d 1/16 in. when it is bent around a cylindrical drum of radius R 24 in. (see figure).
d
R