Questions and Answers of Structural Analysis

Asia contains a complex array of active fault types. As shown in Fig. G-30, for example, there is amajor system of thrust faults in the Himalaya (Himalayan Frontal Thrust), major left-lateral
The data tabulated below were collected within the Basin-and-Range province, from faults in southern Nevada, and from north of Hoover Dam in the Lake Mead area. Although local exceptions exist, the
On the e/time graph in Fig. G-32a (Appendix G) show the strain history of a standard linear solid that would correspond to the stress history in the s/time graph.Fig. G-32a eeeeeeeeeee tr: stress
a. A geologist studying thrust faults in a Proterozoic shear zone in southern Wyoming developed the hypothesis that all of the thrust faults formed during a regional
The rheologic model shown in Fig. 12.15 behaves differently at different strain rates. At high strain rates it behaves elastically (‘‘bounces’’). At moderate strain rates it behaves
Figure G-32b is a sketch of a folded rock layer. The limbs of the folds deformed without fracturing, while fracturing occurred in the hinge zones. In terms of rheologic models, explain why the same
In this problem you will quantitatively explore some rheologic models.1. Using a spring scale and meter stick, graph stress against strain for several rubber bands and springs. Are these perfect
Given the principal stresses of σ1 = 100 MPa (vertical) and σ3 = 20 MPa (horizontal), determine the normal and shear stresses on a fault plane that strikes parallel to σ2 and dips 32° (Plane 1
Plane 1 in Fig. G-33a has been plotted on the Mohr diagram in Fig. G-33b. Determine the normal and shear stresses on planes 2 through 5 and plot them on the Mohr diagram. (Recall that trigonometric
If σ1 is vertical and equal to 50 MPa, and σ3 is horizontal, east–west, and equal to 22 MPa, using a Mohr circle construction determine the normal and shear stresses on a fault striking
The results of four fracture experiments on samples of Rohan Tuff are recorded in the table below.1. Draw Mohr circles for each experiment, and draw the failure envelope.2. Determine the Coulomb
Suppose you are an engineering geologist designing a nuclear waste repository in the Rohan Tuff (see Problem 13.4). Figure 13.11 shows the general plan of the repository. It will be a large room, the
Figure G-34 shows a block of fine-grained limestone that was experimentally shortened by about 1% at room temperature. Four sets of fractures developed. Fractures of sets ‘‘a’’ and
Figure G-35b is a map showing the Johnson Valley Fault in southern California. This is a right-lateral strike-slip fault that lies a short distance to the north of the San Andreas Fault zone. On June
Figure G-36 (Appendix G) contains four photographs of slabs of a breccia from the Alps. The sample in photograph G-36a is undeformed; Fig. G-36b–d show slabs of this same breccia from nearby
Figure G-35a shows the failure envelope of a ‘‘tight’’ (low-permeability) sandstone, which is a petroleum reservoir rock. If σ1 = 72 MPa and σ3 = 42 MPa, determine the amount of pore
Figure 14.2 shows a diagrammatic brachiopod shell before deformation (Fig. 14.2a) and after deformation (Fig. 14.2b).1. Determine the extension e of the hinge line.2. Determine the angular shear C
Figure G-42a is a sketch of a hand specimen of oolite. The orientations of the principal strain axes have been determined in the field on the basis of lineations, cleavages, and the shapes of the
For each of the three photographs in Fig. G-37 do the following:Fig. G-371. Decide which field the strain ellipse lies in, and give your reasons. Refer to Fig. 14.8 for assistance.2. The circle next
Figure G-39 shows a dike and sill complex in which a competent rock, colored black, has intruded into a schist. The horizontal lines represent cleavage in the schist. Consider the cleavage planes to
FigureG-40is aphotographofanexposedbedding plane containing deformed portions of several trilobites.1. Determine the strain ellipse for this rock.2. Determine the 1 + e1: 1 + e2 ratio and the
Redraw the cross section in Fig. 15.4a to make it balanced. Assume that the footwall geometry is correct.Fig. 15.4a Total length, top of: layer 1 = 75 mm layer 2 = 89 mm difference = 14 mm a
For each lettered panel on the cross section in Fig. G- 43 (Appendix G), determine whether the panel in the hanging wall and the footwall directly below is a ramp or a flat. Write the term
Figure 14.15 shows some folds and associated structures produced by coaxial strain. Sketch a similar drawing of structures produced by noncoaxial strain. You may find it useful to use two or three
On the four drawings of deformed rocks in Fig. G-41, indicate the orientations of the principal strain axes. Below each drawing indicate the relative lengths of the axes (e.g., 1 + e1 > 1 + e2 = 1
Use the bed-length technique to restore the cross section in Fig. G-45 and evaluate whether or not it balances. That is, draw the stratigraphic template for the restored cross section below the
What was the principal deformation mechanism in the quartz in the photomicrograph shown in Fig. G- 49 (Appendix G)? What was the principal deformation mechanism in the feldspar? Provide evidence to
You have been hired by an oil company, and your first assignment is to take over a project from another employee. Figure G-48 contains a geologic map and topographic profile of an area that your
Figure G-47 contains a geologic map and topographic profile. Two wells have been drilled in the area, as indicated on the map. Well number 1 encountered a thrust decollement at 1500 m. Well number 2
Let us look more closely at the fault history within Field II of Fig. G-28. We will examine the detailed fault pattern of one small area at Hoover Dam on the Arizona–Nevada border, a highly
Balance the cross section that you evaluated in Problem 15.3. Use the footwall template provided in Fig. G-46. Assume that the footwall structure (i.e., position of ramps and flats) is correct. Use
What was the principal deformation mechanism operative in the rock shown in Fig. G-50? Being careful to use the correct terminology, list the lines of evidence that support your conclusion. Use
On Fig. G-51, label three examples of subgrains and three examples of new grains. Fig. G-51 Photomicrograph for use in Problem 16.3. Crossed polars. Scale bar is 1 mm.
Name the type of fault rock shown in Fig. G-52a, and explain what features you used to identify it. The protolith of this rock was a coarse-grained granite. The irregularly shaped, light-colored
Name the type of fault rock shown in Fig. G-52b, and explain what features you used to identify it. The protolith of this rock was a porphyritic granite. Type of fault rock: Diagnostic features: Fig.
1. Examine the photomicrograph in Fig. G-53. Describe the principal microstructures in the quartz and the feldspar, and interpret the deformation mechanisms that led to these microstructures.2. What
1. Figure G-54a shows a porphyroclast. What type is it?2. The shear zone that contains this porphyroclast strikes 050° and dips 70° to the southeast. Mineral lineations plunge 70° toward 140°
Figure G-55 is a tectonic map of a region that contains three major shear zones that were active at different times. For each shear zone a stereogram is provided that indicates the foliation and
Figure G-54b is a field photograph of a mylonitic megacrystic (porphyritic) granite from a shear zone that strikes 330° and dips 20°SW. Mineral lineations are down dip. You are looking at a
The map in Fig. G-61 depicts the ‘‘present-day’’ distribution of hypothetical continents and oceans. The map contains geologic information as well as seismicity patterns, focal-mechanism
Paleomagnetic determinations were conducted on three suites of rocks from the Bree Creek Quadrangle. A sandstone unit within the 60 Ma Edoras Formation yielded average inclinations of 46°;
Figure G-59 contains a map showing the position of the Mendocino triple junction off the coast of northern California. The Mendocino triple junction is the point of intersection of the Pacific, North
The distance between magnetic anomalies number 12 (34 Ma) and 23 (52 Ma) on a single oceanic plate is 810 km. What is the time-averaged rate of spreading across the ridge during this interval?
Determine the inclination of the earth’s magnetic field at the following latitudes:20°N45°S78°N10°S.
Sketch the focal-mechanism solutions for earthquakes that would be expected to occur at each of the plate boundaries in Problems 17.1 and 17.2 (Fig. G-57). Be sure to label the fault plane, the
Given the plate configuration shown in Fig. G-57b, determine the type of plate boundary and the relative rate of motion between plates B and C.Fig. G-57b 3 cm/yr b Plate B Plate A Plate с A 8.4
Given the plate tectonic configuration shown in Fig. G-57a (Appendix G), determine the type of plate boundary and the relative rate of motion between plates B and C. Plate A 6 cm/yr 4.5
Use a computer program to determine the reactions on the frame. Assume A, B, D, and F are pins. AE and EI are constant. 8 kN B 8 m 4 m 6 m
Use a computer program to determine the reactions on the frame. AE and EI are constant. 1.5 k/ft 15 k- 20 ft D 24 ft
Use a computer program to determine the reactions on the beam. Assume A and D are pins and B and C are rollers. EI is constant. 3 k/ft те De -20 ft- -8 ft- -8 ft
Use a computer program to determine the reactions on the beam. Assume A is fixed. EI is constant. 12 k 4 k/ft 'A -8 ft --8 ft→ - 20 ft- -15 ft-
Use a computer program and determine the reactions on the truss and the force in each member. AE is constant. Fe gost 4 kN 2 m -2 m-
Use a computer program and determine the reactions on the truss and the force in each member. AE is constant. 2 k 1.5 k लি 6 ft 6 ft 6 ft E8 ft- -8 ft- -8 ft-
Solve the equations in Prob. A–20 using the Gauss elimination method.Data From Prob. A-20x1 + 2x2 - 2x3 = 5, x1 - x2 + x3 = -1, x1 - x2 - x3 = 1 using the
Solve the equations x1 + 2x2 - 2x3 = 5, x1 - x2 + x3 = -1, x1 - x2 - x3 = 1 Using the matrix equation x = A-1 C.
Solve the equations in Prob. A–18 using the Gauss elimination method.Data From Prob. A-184x1 + x2 + x3 = -1, -5x1 + 4x2 + 3x3 = 4, x1 - 2x2 + x3 = 2 Using the
Solve the equations 4x1 + x2 + x3 = -1, -5x1 + 4x2 + 3x3 = 4, x1 - 2x2 + x3 = 2 Using the matrix equation x = A-1 C.
Ifdetermine A-1. 3 A = 4 -1 2 3
Ifdetermine A-1. 5] [2 A 4 -1
Evaluate the determinants and 4 3 -1 6 5 7 2 1 8 2 -1 4
Show that the associative law is valid, i.e,, A(BC) = (AB)C, if 2 5 0. - 5 6 в -1 4
Show that the distributive law is valid, i.e,, A(B+C) = AB + AC if 4 2 A [3 5 6. 2 B = -1
Ifanddetermine AB. Г A =| 0 3 6 5 -1 2 1 4 Г2 -1 -1 B = 3 2 5 6. 4,
Ifanddetermine AB. 2 5 A 2. 2 B = 5 -1
Ifanddetermine AB. 5 A 3. -1 2 3 2 в -1
Ifdetermine AAT. 2 8 5]' A -1
Ifdetermine AAT. -1
Ifdetermine A + AT. 2 3 6 5 9 2 2. -1
If andshow that (A + B)T = AT + BT. A =| 5 B = 4
Ifand determine AB. A = -5 6. B = [4 6 -5],
Ifand determine AB. Г6 3] A [4 2. Г6 B 2 [5 -1.
Ifanddetermine AB. A = [2 5] %3D 4 B = 2 -1 -2
Ifand determine 3A - 2B and A -2B. 5 -2 A = | 4 -1 3. 3. 6 4 -3 B =| 3 2 -2 5 1
If and Determine 2A - B and A + 3B. 6. A = | 2 4 -2 3. -1 2 B = 5 8 -2
Determine the support reactions at the pins ‘ and ž‚. Take E = 29(103) ksi, I = 700 in4, A = 20 in2for each member. (3. 16 ft 20 k - 12 ft - 3 12 ft - -8 2)
Determine the structure stiffness matrixKfor the frame. Take E = 29(103) ksi, I = 700 in4, A = 20 in2for each member. 6. 2 16 ft 20 k - 12 ft- 3. 12 ft
Determine the support reactions at ‘ and ž‚. Take E = 29(103) ksi, I = 300 in4, A = 10 in2for each member. 2 k/ft A7 42 (2 6. 2 (3 3 20 ft 10 ft 8.
Determine the stiffness matrix K for the frame. Take E = 29(103) ksi, I = 300 in4, A = 10 in2for each member. 2 k/ft 12 17 2 (3. 3 20 ft 10 ft 5.
Determine the components of displacement at ‘ . Take E = 29(103) ksi, I = 650 in4, A = 20 in2for each member. 5 3 4 4 k- 2 12 ft (3) 10 ft
Determine the structure stiffness matrixK for the frame. Take E = 29(103) ksi, I = 650 in4, A = 20 in2for each member. 5 4 k- 12 ft (3 -10 ft 2.
Determine the support reactions at pins ‘ and ž‚. Take E = 200 GPa, I = 350(106) mm4, A = 15(103) mm2for each member. 2 60 kN 3 - 2 m– 2 m 4 m 3) 9
Determine the structure stiffness matrixK for the frame. Take E = GPa, I = 350(106) mm4, A = 15(103) mm2for each member. Joints at ‘ and ž‚ are pins. 2 60 kN 3 |1 2) 2 m - -
Determine the support reactions at ‘ and ž‚. Take E = 200 MPa, I = 300(106) mm4, A = 21(103) mm2for each member. - 5 m 300 kN · m, 3 9. (2, 4 m 2
Determine the structure stiffness matrixKfor the frame. Assume ž‚ is pinned and ‘ is fixed. Take E = 200 MPa, I = 300(106) mm4, A = 21(103) mm2for each member. 5 m-
Determine the support reactions at the fixed supports ‘ and ž‚. Take E = 200 GPa, I = 300(106) mm4, A = 10(103) mm2 for each member. 12 kN/m 1) 2 m - 4 m- 10 kN 2 m 6.
Determine the structure stiffness matrixK for the frame. Assume ‘ and ž‚ are fixed. Take E = 200 GPa, I = 300(106) mm4, A = 10(103) mm2for each member. 12 kN/m 1) 2 m - 4 m-
Determine the moments at ‘ and ‘¢. Assume ‘¡ is a roller and ‘ and ‘¢ are fixed. EI is constant. 5 25 kN/m 3. 2 3. 6 m 4 m
Determine the reactions at the supports. EI is constant. 5 15 kN/m 2 2 | 1 3 (1) 2) 3. 3 m- 4 m
Determine the moments at ‘ and ‘¢ if the support ‘¡ moves upward 5 mm. Assume ‘¡ is a roller and ‘ and ‘¢ are fixed. EI = 60(106)
Determine the reactions at the supports. Assume the rollers can either push or pull on the beam. EI is constant. 6. 3 6 kN/m 20 kN-m (1) (3 8 m- -12 m-
Determine the reactions at the supports. Assume ‘ is a pin and ‘¡ and ‘¢ are rollers that can either push or pull on the beam. EI is constant. 7A 84 3k 64 4 3 3
Determine the support reactions. Assume ‘¡ and ‘¢ are rollers and ‘ is a pin. EI is constant. 15 kN/m 5 3 2 1) 8 m 6 m 2.
Determine the reactions at the supports. Assume ‘ is fixed ž and ‘¢ are rollers. EI is constant. 3 10 kN/m 4 2 -6 m 8 m
Determine the reactions at the supports. Assume ‘ and ‘¢ are fixed and ‘¡ is a roller. EI is constant. 3 9 kN/m 6 kN/m 2 4 m - 6 m
Determine the moments at ‘¡ and ‘¢. EI is constant. Assume ‘ , ‘¡, and ‘¢ are rollers and ‘£ is pinned. 4 kN/m प স (2) ত 2 3
Determine the reactions at the supports. Assume ‘¡ is pinned and ‘ and ‘¢ are rollers. EI is constant. 5 3 k/ft 6 2 3 21 -4 ft - - 4 - 8 ft 8 ft ft -
Determine the reactions at the supports. There is a smooth slider at ‘ . EI is constant. 30 kN/m (2. |1 (2 4 m-
Determine the stiffness matrixKfor the truss. Take A = 0.0015 m2and E = 200 GPa for each member. 2 m 2 m- 4 10 2 m 4 30 kN
Determine the stiffness matrixKfor the truss. Take A = 0.0015 m2and E = 200 GPa for each member. 410 44 20 kN 6. -4 m -4 m
Determine the stiffness matrixKfor the truss. AE is constant. 3 m- 2 -1 3 kN 4 m 45°

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