Properties of Sections
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1 ARCH 314 Structures I Test Primer Questions Dr.-Ing. Peter von Buelow Properties of Sections 1. Select all that apply to the characteristics of the Center of Gravity: A) 1. The point about which the body is stable or balanced 2. The point of application of the resultant weight 2. Sketch the center of area for the following body shapes: A) 3. What is generally known about the centroid of an area with two axes of symmetry. A) The area has one centroid at the crossing of the axes. 4. Diagram shown demonstrates the location of centroid of simple triangle with the given dimension. Find the centroidal x and y distances as shown on the diagram. A) x = 12" 3 = 4" y = 6" 3 = 2" 5. What sectional properties are computed using the centroid as a reference? A) Static Moment of Area, Moment of Inertia, Section Modulus 6. What does the center of gravity of a mass theoretically represent? A) The point at which the entire mass or area can be considered to be concentrated. The point at which the mass could be held and be in balance in all directions. 7. The centroid of an area is not always located within the bounds of the area. (T or F) A) true
2 Arch 314 Chapter 6 Primer Questions Page 2 of 3 Moment of Inertia Ch The Moment of Inertia is a gage of what? A) Cross sectional stiffness. 2. For any cross section, which of the following changes will increase the moment of inertia? A) Increase the depth, without changing the area Increase the width, by adding area Increase the area in any way 3. For two beams of equal span, material and loading, if beam A has a moment of inertia of 1000 in 4, and beam B has a moment of inertia of 2000 in 4 A) A will deflect more than B 4. Which of the configurations of the 3 2x6's (full dimension) would give the highest moment of inertia? A) A 5. What is the moment of inertia for section C above? A) 108 in 4 6. A beam loaded flat wise is less stiff than the same beam loaded edge wise. This is primarily because? A) The moment of inertia is greater for the greater depth 7. What is the equation for calculating the moment of inertia of a rectangle? A) I = (bh^3)/12 8. Which orientation of the same cross-section has the larger moment of inertia?
3 Arch 314 Chapter 6 Primer Questions Page 3 of 3 A) The cross-section at the left 9. Calculate the moment of inertia of the following shape: A) 10. Determine whether the following is true about Radius of Gyration: The larger the radius of gyration, the more resistant the section is to buckling. A) True 11. In order to find the moment of inertia about the major centroidal X axis for the cross section shown below, the perpendicular distances between the major centroidal X axis and the parallel axis that passes through the centroid of each component are required. Determine the distances, dy1, dy2 and dy3 for each component. A) d y1 = 6" 2-1" 2 = 2.5" d y2 = 0" d y3 = 6" 2-1" 2 = 2.5" 12. The following tables have been constructed to calculate the moment of inertia for the cross section shown. Using the given information in the tables, determine the major centroidal axes from the reference origin and the moment of inertia of the total cross-section about the major centroidal x and y axis.
4 Arch 314 Chapter 6 Primer Questions Page 4 of 3 A) y = SyDA A = 341.6in3 26.5in 2 =12.9" I x = SI xc + S(A d y 2 ) = 809in in 4 =1,305in 4 I y = SI yc + S(A d x 2 ) = 389in 4 + 0in 4 = 389in What theorem provides a simple way to compute moment of inertia of composite areas? A) Parallel Axis Theorem 14. Which shape has a greater moment of inertia with respect to the x-x axis? A) A A) B) 15. A centroid of area is similar in concept to a A) Center of gravity.
5 Arch 314 Chapter 6 Primer Questions Page 5 of Areas with one axis of symmetry A) Have only one centroid, which will always lie somewhere on the axis 17. What it the distance to the centroidal axis, y-bar, for the section shown below? A) 6" y 18. What is the moment of inertia, Ix for the section at the right? A) 326 in 4 1" 4" 1" 19. What is the moment of inertia, Iy for the section above? x x 12" A) 29.5 in 4 y -b a r 1" y 4" 20. What is the radius of gyration for a solid circular section with a radius of 4"? A) 2" 21. Two circular sections have the same area. One is solid and one is hollow. The radius of gyration for the solid section is A) is less than that of the hollow section.
6 Arch 314 Chapter 6 Primer Questions Page 6 of The four illustrations below describe the sign convention for shear and moment in beams. Match the illustration to the descriptions at the left.. positive shear (A) B positive moment (A) C negative shear (A) A negative moment (A) D 23. Which is true about the steel I beam shown? flange web A) The web holds the flanges apart and resists some shear. 24. True/False The term neutral axis refers to a longitudinal axis on a beam in bending that experiences neither tension nor compression stresses. (A) T
7 Arch 314 Chapter 6 Primer Questions Page 7 of With the given cross section and its neutral axis, find the bending stress in BOTH the extreme compression fibers and the extreme tension fibers at the MIDPOINT of the beam. A uniform load of 2 k/ft is applied to the beam as shown. ksi ksi Compression Tension 26. Find the Moment of Inertia of the section shown below with respect to the neutral axis.
8 Arch 314 Chapter 6 Primer Questions Page 8 of A steel wide flange section W6x25 has an Ix = 53.4 IN 4. How deep would a 4 wide, rectangular piece of basswood have to be to attain the same geometric stiffness, Ix? Esteel = ksi Ewood = 1400 ksi A) 5.43 IN 28. A point loaded beam has section shown below. Fill the blanks with : ft, fc, ct, cc, and neutral axis ft fc ct cc NA Maximum internal tension stress Maximum internal compression stress The controlling tension extreme fiber distance The controlling compression extreme fiber distance Neutral axis fc cc NA ct ft 29. When allowable stress for tension and compression is equal, which of the description below is true for the load on the beam above? A) Maximum tension stress is greater
9 Arch 314 Chapter 6 Primer Questions Page 9 of Following are sections of beam. Which of them has the largest moment of inertia ( xx)? Material is homogeneous. Answer could be more than one. (A) B, D 31. For the hollow pipe section shown at right the centroid of area is A. at the center of the pipe 32. The two methods commonly used to calculate the centroid of area are A. addition and subtraction 33. For a homogenous, symmetric T shown, the center of gravity can be found by inspection (without calculation) for the coordinates in A) x and y only
10 Arch 314 Chapter 6 Primer Questions Page 10 of Which of the pictured sections has the largest moment of inertia (I) about the N.A. shown? (A) D 35. Given the rectangular section shown below, what is the resulting maximum bending stress (in psi) under a load producing a maximum moment of 5000 ft-lbs? I = 72 in 4 (A) 2500 psi 36. The Moment of Inertia is a gage of? A) Cross sectional stiffness. 37. The stiffness of a cross-section is described by? A) Moment of Inertia ( )
11 Arch 314 Chapter 6 Primer Questions Page 11 of What effect does the hole have on the centroid of the section? A) Shifts it upward 39. For each pair of cross sections, which has a greater moment of inertia with respect to the axis show? The drawings are to scale and each cross section has the same total area. A) A & B have the same moment of inertia A) Moment of inertia of B is greater 40. For the beam show in elevation, compare the differences of fiber stress and moment for the two possible beam shapes shown in section. Note: section A and B have the same areas and depths. (A) The maximum fiber stress in section A would be less (more/less/same) than section B. The maximum moment in section A would be the same (more/less/same) than section B.
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