EXAM1-Solution-Fall-2023-10-23.pdf

10/23/2023 1 Online Distributed Midterm Exam Kurt McMullin CE164 – Fall 2023 A 15 ft The only load on the beam is a Dead Load which is the three point loads of 10 kips each. The two point loads are halfway between Point A and Point B and halfway between Point B and Point C. There is no Live Load on the frame. Determinant Continuous Beam P 15 ft B C The internal hinges are 3 feet from Points B and C Points A and B are pin supports. Point C is a fixed support. Calculate three things. The Reaction at B. The Shear 1’ to the right of B. The Moment at B. P P Engr Fundamentals RB = (1/15){10*7.5 + 10*15 + 5*18} = 21 kips VB = 5 kips MB = 5*3 = 15 kip-ft.

10/23/2023 2 A 15 ft The only load on the beam is a Dead Load which is the three point loads of 5 kips each. The two point loads are halfway between Point A and Point B and halfway between Point B and Point C. There is no Live Load on the frame. Determinant Continuous Beam P 15 ft B C The internal hinges are 3 feet from Points B and C Points A and B are pin supports. Point C is a fixed support. Calculate three things. The Reaction at B. The Shear 1’ to the right of B. The Moment at B. P P Engr Fundamentals RB = (1/15){5*7.5 + 5*15 + 2.5*18} = 10.5 kips VB = 2.5 kips MB = 2.5*3 = 7.5 kip-ft. A 15 ft The only load on the beam is a Dead Load which is the three point loads of 5 kips each. The two point loads are halfway between Point A and Point B and halfway between Point B and Point C. There is no Live Load on the frame. Determinant Continuous Beam P 15 ft B C The internal hinges are 3 feet from Points B and C Points A and B are pin supports. Point C is a fixed support. Calculate three things. The Reaction at B. The Shear 1’ to the left of B. The Moment at B. P P Engr Fundamentals RB = (1/15){5*7.5 + 2.5*18} = 5.5 kips VB = 2.5 kips MB = 2.5*3 = 7.5 kip-ft.

10/23/2023 3 A 15 ft The only load on the beam is a Dead Load which is the three point loads of 10 kips each. The two point loads are halfway between Point A and Point B and halfway between Point B and Point C. There is no Live Load on the frame. Determinant Continuous Beam P 15 ft B C The internal hinges are 3 feet from Points B and C Points A and B are pin supports. Point C is a fixed support. Calculate three things. The Reaction at B. The Shear 1’ to the right of B. The Moment at B. P P Engr Fundamentals RB = (1/15){10*7.5 + 5*18} = 11.0 kips VB = 5 kips MB = 5*3 = 15.0 kip-ft. TOP VIEW BOLTED CONNECTION 3x8 2x10 SIDE VIEW The Dead Load force applied to the assembly is 8 kips. Each bolt can resist 2.5 kips parallel to the grain and 1 kip perpendicular to the grain. Calculate the net area of the 2x10. Calculate the tension stress on the 2x10. Calculate the strength, Z’, of the assembly if we only consider the bolt strength of the 2x10. SAWN LUMBER – All bolts are 7/8” diameter DEAD LOAD 30 degrees Anet = 13.88 – 2(7/8 + 1/8)(1.5) = 10.88 sq inch ft = 8000 / 10.88 = 735 psi Z’ = 0.9(6)(2.5) = 13.5 kips

10/23/2023 4 TOP VIEW BOLTED CONNECTION 3x8 2x10 SIDE VIEW The Dead Load force applied to the assembly is 6 kips. Each bolt can resist 2 kips parallel to the grain and 1.5 kips perpendicular to the grain. Calculate the net area of the 2x10. Calculate the tension stress on the 2x10. Calculate the strength, Z’, of the assembly if we only consider the bolt strength of the 2x10. SAWN LUMBER DEAD LOAD 30 degrees Anet = 13.88 – 2(7/8 + 1/8)(1.5) = 10.88 sq inch ft = 6000 / 10.88 = 551 psi Z’ = 0.9(6)(2) = 10.8 kips 7/8” Diameter Bolts TOP VIEW BOLTED CONNECTION 3x8 2x10 SIDE VIEW The Dead Load force applied to the assembly is 8 kips. Each bolt can resist 2.5 kips parallel to the grain and 1 kip perpendicular to the grain. Calculate the net area of the 2x10. Calculate the tension stress on the 2x10. Calculate the strength, Z’, of the assembly if we only consider the bolt strength of the 2x10. SAWN LUMBER – All bolts are 3/4” diameter DEAD LOAD 30 degrees Anet = 13.88 – 2(3/4 + 1/8)(1.5) = 11.23 sq inch ft = 8000 / 11.23 = 712 psi Z’ = 0.9(6)(2.5) = 13.5 kips

10/23/2023 5 TOP VIEW BOLTED CONNECTION 3x8 2x10 SIDE VIEW The Dead Load force applied to the assembly is 8 kips. Each bolt can resist 2.5 kips parallel to the grain and 1 kip perpendicular to the grain. Calculate the net area of the 2x10. Calculate the tension stress on the 2x10. Calculate the strength, Z’, of the assembly if we only consider the bolt strength of the 2x10. SAWN LUMBER – All bolts are 1/2” diameter DEAD LOAD 30 degrees Anet = 13.88 – 2(1/2 + 1/8)(1.5) = 12.01 sq inch ft = 8000 / 12.01 = 666 psi Z’ = 0.9(6)(2.5) = 13.5 kips TOP VIEW NAILED CONNECTION 2x8 4x10 SIDE VIEW SAWN LUMBER The stars represent 16d nails. The nails are 0.22 inch diameter and 3.5 inches long. The yield stress is 90 ksi. DEAD LOAD Calculate the strength of a single nail (Z) considering the bearing strength of both wood pieces is 3000 psi. Consider only modes I and IV. Rd = KD = 10(0.22) + 0.5 = 2.7 Mode I Main = (0.22)(2)(3000)/2.7 = 489 lbs. Side = (0.22)(1.5)(3000)/2.7 = 367 lbs. Mode IV - for Re = 1 Z = (0.22)^2/2.7 * sqrt{2*3000*90000/(3*2)} = 170 lbs Z = 170 lbs .

10/23/2023 6 TOP VIEW NAILED CONNECTION 2x8 4x10 SIDE VIEW SAWN LUMBER The stars represent 16d nails. The nails are 0.22 inch diameter and 4.0 inches long. The yield stress is 90 ksi. DEAD LOAD Calculate the strength of a single nail (Z) considering the bearing strength of both wood pieces is 2000 psi. Consider only modes I and IV. Rd = KD = 10(0.22) + 0.5 = 2.7 Mode I Main = (0.22)(2.5)(2000)/2.7 = 407 lbs. Side = (0.22)(1.5)(2000)/2.7 = 244 lbs. Mode IV - for Re = 1 Z = (0.22)^2/2.7 * sqrt{2*2000*90000/(3*2)} = 140 lbs Z = 140 lbs . TOP VIEW NAILED CONNECTION 2x8 4x10 SIDE VIEW SAWN LUMBER The stars represent 16d nails. The nails are 0.20 inch diameter and 4.0 inches long. The yield stress is 90 ksi. DEAD LOAD Calculate the strength of a single nail (Z) considering the bearing strength of both wood pieces is 2000 psi. Consider only modes I and IV. Rd = KD = 10(0.20) + 0.5 = 2.5 Mode I Main = (0.20)(2.5)(2000)/2.5 = 400 lbs. Side = (0.20)(1.5)(2000)/2.5 = 240 lbs. Mode IV - for Re = 1 Z = (0.20)^2/2.5 * sqrt{2*2000*90000/(3*2)} = 125 lbs Z = 125 lbs .

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