Problem 2 (60 points): Develop the complete interaction diagram for a 9,000 psi, 20-inch round column with eight #7 Grade 60 bars. Assume #4 spirals with a 5-inch pitch and 1.5-inch clear cover. The eight longitudinal bars are to be equally spaced along the perimeter of the column. Plot the interaction curves both factored and unfactored. Include the primary 5 cases. For each case (A through E) draw and label the strain diagram through the cross section and then the summary of the forces through the cross section. Last, draw the cross-section of the column to scale and label as needed. Hints: The compression block for a round column will be segment of a circle so you will need to figure out the geometry on how to calculate that area and the centroid of that area. However, the calculation of c and a will remain the same. You can design it about either the weak axis or the strong axis, as they should give very similar results. Its recommended to solve for the axis that makes the geometry easiest to solve for (FYI, in practice one would only solve for the weak axis results). Last, dont forget that the factors are different for spiral columns as opposed to tied columns. In addition, the ACI equation to determine Pnmax has a different factor for spiral columns as opposed to tied columns. Mathcad Hints: If you are using Mathcad to solve this one, the trigonometric functions (sin and cosine) that would will need to solve for the area and centroid of the segment of the circle are located under the Functions tab, then to the right for fx, All Functions, then search under for trigonometric under the lefthand column that will appear. The default for angles in Mathcad is radians (not degrees). 1 radian = 1800 /

Problem 2 (60 points): Develop the complete interaction diagram for a 9,000 psi, 20-inch round column with eight #7 Grade 60 bars. Assume #4 spirals with a 5-inch pitch and 1.5-inch clear cover. The eight longitudinal bars are to be equally spaced along the perimeter of the column. Plot the interaction curves both factored and unfactored. Include the primary 5 cases. For each case (A through E) draw and label the strain diagram through the cross section and then the summary of the forces through the cross section. Last, draw the cross-section of the column to scale and label as needed. Hints: The compression block for a round column will be segment of a circle so you will need to figure out the geometry on how to calculate that area and the centroid of that area. However, the calculation of 'c' and a' will remain the same. You can design it about either the weak axis or the strong axis, as they should give very similar results. It's recommended to solve for the axis that makes the geometry easiest to solve for (FYI, in practice one would only solve for the weak axis results). Last, don't forget that the factors are different for spiral columns as opposed to tied columns. In addition, the ACI equation to determine Pnmax has a different factor for spiral columns as opposed to tied columns. Mathcad Hints: If you are using Mathcad to solve this one, the trigonometric functions (sin and cosine) that would will need to solve for the area and centroid of the segment of the circle are located under the Functions tab, then to the right for 'fx, All Functions', then search under for trigonometric' under the left- hand column that will appear. The default for angles in Mathcad is radians (not degrees). 1 radian = 180/r. Problem 2 (60 points): Develop the complete interaction diagram for a 9,000 psi, 20-inch round column with eight #7 Grade 60 bars. Assume #4 spirals with a 5-inch pitch and 1.5-inch clear cover. The eight longitudinal bars are to be equally spaced along the perimeter of the column. Plot the interaction curves both factored and unfactored. Include the primary 5 cases. For each case (A through E) draw and label the strain diagram through the cross section and then the summary of the forces through the cross section. Last, draw the cross-section of the column to scale and label as needed. Hints: The compression block for a round column will be segment of a circle so you will need to figure out the geometry on how to calculate that area and the centroid of that area. However, the calculation of 'c' and a' will remain the same. You can design it about either the weak axis or the strong axis, as they should give very similar results. It's recommended to solve for the axis that makes the geometry easiest to solve for (FYI, in practice one would only solve for the weak axis results). Last, don't forget that the factors are different for spiral columns as opposed to tied columns. In addition, the ACI equation to determine Pnmax has a different factor for spiral columns as opposed to tied columns. Mathcad Hints: If you are using Mathcad to solve this one, the trigonometric functions (sin and cosine) that would will need to solve for the area and centroid of the segment of the circle are located under the Functions tab, then to the right for 'fx, All Functions', then search under for trigonometric' under the left- hand column that will appear. The default for angles in Mathcad is radians (not degrees). 1 radian = 180/r