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Cee 312(4)(structural analysis)

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CEE-312 Structural Analysis and Design Sessional-I (1.0 credit) Lecture: 4 Bijit Kumar Banik Assistant Professor, CEE, SUST Room No.: 115 (“C” building) bijit_sustbd@yahoo.com Department of Civil and Environmental Engineering
Analysis and design of an Industrial roof truss system (4.41) (4.41) (3.53) (3.53) (4.41) (4.41) (- 5.05) (- 4.04) (- 3.03) (- 3.03) (- 4.04) (- 5.05) 6@6 ft = 36 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 2.94 k2.94 k (.18) (0.67) (0.67) (.18) (2.14) (-1.32) (- 1.01) (-1.32) (- 1.01)
Analysis and design of an Industrial roof truss system P = (0.07*29.05-2.1)*25.6 = -1.7 psf For windward surface For leeward surface P = -0.7*25.6 = -17.92 psf We already calculated in lecture-2 Once again what –ve sign means? Suction/Uplift Wind load calculations
Wind Load Analysis 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft Wind blows from left to right Windward side joint loads (U1 & U2)= 1.7*20*6.86 = 0.23k End joint loads [ L0 & (U3)left ] = 0.23/2 = 0.12k Leeward side joint loads (U4 & U5)=17.92*20*6.86 = 2.46k End joint loads [ L6 & (U3)right ] = 2.46/2 = 1.23k 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k
6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft –0.23*6.86 –0.23*2*6.86 –0.12*3*6.86 –1.23*(9/10.3)*18 +1.23*(5/10.3)*10 –2.46*(9/10.3)*24 +2.46*(5/10.3)*2*(10/3) – 2.46*(9/10.3)*30 +2.46*(5/10.3)*(10/3) – 1.23*(9/10.3)*36 + R1*36 = 0 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k ∑ML0= 0 +ve 5 9 10.3 9 5 10.3 R1 = 4.54k = 4.54k Wind Load Analysis
6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft R2 = (9/10.3)*(2*0.12+2*0.23+2*1.23+2*2.46) – 4.54 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k ∑V= 0 5 9 10.3 9 5 10.3 R2 = 2.60k H = (5/10.3)*(2*1.23+2*2.46) – (5/10.3)*(2*0.12+2*0.23) ∑H= 0 H = 3.24k = 3.24k = 2.60k = 4.54k Wind Load Analysis
6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 1 1 ∑V = 0 (5/10.3)*L0U1+(9/10.3)*0.12 – 2.6 = 0 L0U1= 5.14 k (T) 5 9 10.3 ∑H = 0 L0L1 +(9/10.3)*5.14 – (5/10.3)*0.12 – 3.24 =0 L0L1= 1.19 k (C) 2.60 k 0.12k L0L1 L0U1 1-1 3.24 k 9 5 10.3 Wind Load Analysis
∑V= 0 L1U1 = 0 L1L2 = L0L1 = 1.19k (C) ∑H= 0 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 2 2 L1L2 2-2 L0L1=1.19k L1U1 Wind Load Analysis
6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 3 3 9 510.3 9 5 10.3 9 5 10.3 ∑ML0 = 0 – 0.23*6.86 + (5/10.3)*U1L2*6 + (9/10.3)*U1L2*(10/3)= 0 U1L2= 0.27 k (T) ∑V = 0 (9/10.3)*0.12+(9/10.3)*0.23 + (5/10.3)*U1U2 – (5/10.3)*0.27 – 2.60= 0 U1U2= 5.0 k (T) +ve 3-3 U1 L0 L1 L2 U2 0.23 k 0.12 k 2.60 k (10/3)’ 1.19k3.24k Wind Load Analysis
6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 4 4 ∑H = 0 L2L3= 0.95 k (C) 5 9 10.3 L2L3 4-4 1.19k L2U2 0.27k ∑V = 0 L2U2 = (5/10.3)*0.27 L2U2= 0.13 k (C) L2L3 +1.19 – (9/10.3)*0.27 = 0 Wind Load Analysis
6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 5 5 10 9 13.45 5 9 10.3 ∑ML0 = 0 (9/13.45)*U2L3*(20/3)+ (10/13.45)*U2L3*12 – 0.23*6.86 – 0.23*2*6.86 = 0 U2L3= 0.35 k (T) ∑V = 0 (5/10.3)*U2U3+ (9/10.3)*(0.12+0.23+0.23) – (10/13.45)*0.35 – 2.60 = 0 U2U3= 4.85 k (T) +ve 9 5 10.3 5-5 L0 L1 L2 L3 U1 U2 U3 0.12 k 2.60 k 0.23 k 0.95 k 2*(10/3) 0.23 k 3.24 k Wind Load Analysis
(5/10.3)*U5L6+(9/10.3)*1.23 – 4.54 = 0 ∑V= 0 U5L6 = 7.14k (T) ∑H= 0 L5L6 = 5.64k (C) 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 6 6 5 9 10.3 5 9 10.3 4.54 k U5L6 1.23k 6-6 L5L6(5/10.3)*1.23 – (9/10.3)*7.14 – L5L6= 0 Wind Load Analysis
6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 7 7 ∑H = 0 5.64k 7 – 7 L4L5 L5U5 ∑V = 0 L5U5= 0 L4L5 = 1.19k (C) Wind Load Analysis
6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 8 8 5 9 10.3 9 510.3 9 5 10.3 L6 U5 L5L4 U4 2.46k 1.23k 4.54k 8-8 ∑ML6 = 0 2.46*6.86 – (5/10.3)*U5L4*6 – (9/10.3)*U5L4*(10/3)= 0 U5L4= 2.90 k (T) ∑V = 0 (9/10.3)*2.46+(9/10.3)*1.23 + (5/10.3)*U4U5 – (5/10.3)*2.90 – 4.54= 0 U4U5= 5.61 k (T) +ve Wind Load Analysis
6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 9 9 ∑H = 0 L3L4= 3.11 k (C) ∑V = 0 L4U4 = (5/10.3)*2.90 L4U4= 1.41 k (C) L3L4+ (9/10.3)*2.90 – 5.64 = 0 9 510.3 5.64k 9-9 L4U4 2.90k L3U4 Wind Load Analysis
6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 10 10 9 5 10.3 9 10 13.45 9 5 10.3 2.46k 2.46k 1.23k 4.54k L6L5L4L3 U3 U5 U4 3.11k 10 -10∑ML6 = 0 –(9/13.45)*U4L3*(20/3) – (10/13.45)*U4L3*12 + 2.46*6.86 +2.46*2*6.86 = 0 U4L3= 3.78 k (T) ∑V = 0 (5/10.3)*U3U4 + (9/10.3)*(1.23+2*2.46) – (10/13.45)*3.78 – 4.54 = 0 U3U4= 4.07 k (T) +ve Wind Load Analysis
6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 11 11 ∑V = 0 9 10 13.45 9 10 13.45 3.11k 11 – 11 0.95k L3U3 L3 0.35k 3.78k(10/13.45)*3.78 + (10/13.45)*0.35 – L3U3= 0 L3U3= 3.07 k (C) Wind Load Analysis
(- 1.19) (-1.19) (-0.95) (-3.11) (-5.64) (-5.64) (5.14) (5.00) (4.85) (4.07) (5.61) (7.14) 6@6 ft = 36 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 4.54 k2.60 k (0) (-0.13) (-1.41) (0) (-3.07) (0.35) (0.27) (3.78) (2.90) 3.24k L R Wind Load Analysis
Cee 312(4)(structural analysis)

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Cee 312(4)(structural analysis)

  • 1. CEE-312 Structural Analysis and Design Sessional-I (1.0 credit) Lecture: 4 Bijit Kumar Banik Assistant Professor, CEE, SUST Room No.: 115 (“C” building) bijit_sustbd@yahoo.com Department of Civil and Environmental Engineering
  • 2. Analysis and design of an Industrial roof truss system (4.41) (4.41) (3.53) (3.53) (4.41) (4.41) (- 5.05) (- 4.04) (- 3.03) (- 3.03) (- 4.04) (- 5.05) 6@6 ft = 36 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 2.94 k2.94 k (.18) (0.67) (0.67) (.18) (2.14) (-1.32) (- 1.01) (-1.32) (- 1.01)
  • 3. Analysis and design of an Industrial roof truss system P = (0.07*29.05-2.1)*25.6 = -1.7 psf For windward surface For leeward surface P = -0.7*25.6 = -17.92 psf We already calculated in lecture-2 Once again what –ve sign means? Suction/Uplift Wind load calculations
  • 4. Wind Load Analysis 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft Wind blows from left to right Windward side joint loads (U1 & U2)= 1.7*20*6.86 = 0.23k End joint loads [ L0 & (U3)left ] = 0.23/2 = 0.12k Leeward side joint loads (U4 & U5)=17.92*20*6.86 = 2.46k End joint loads [ L6 & (U3)right ] = 2.46/2 = 1.23k 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k
  • 5. 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft –0.23*6.86 –0.23*2*6.86 –0.12*3*6.86 –1.23*(9/10.3)*18 +1.23*(5/10.3)*10 –2.46*(9/10.3)*24 +2.46*(5/10.3)*2*(10/3) – 2.46*(9/10.3)*30 +2.46*(5/10.3)*(10/3) – 1.23*(9/10.3)*36 + R1*36 = 0 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k ∑ML0= 0 +ve 5 9 10.3 9 5 10.3 R1 = 4.54k = 4.54k Wind Load Analysis
  • 6. 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft R2 = (9/10.3)*(2*0.12+2*0.23+2*1.23+2*2.46) – 4.54 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k ∑V= 0 5 9 10.3 9 5 10.3 R2 = 2.60k H = (5/10.3)*(2*1.23+2*2.46) – (5/10.3)*(2*0.12+2*0.23) ∑H= 0 H = 3.24k = 3.24k = 2.60k = 4.54k Wind Load Analysis
  • 7. 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 1 1 ∑V = 0 (5/10.3)*L0U1+(9/10.3)*0.12 – 2.6 = 0 L0U1= 5.14 k (T) 5 9 10.3 ∑H = 0 L0L1 +(9/10.3)*5.14 – (5/10.3)*0.12 – 3.24 =0 L0L1= 1.19 k (C) 2.60 k 0.12k L0L1 L0U1 1-1 3.24 k 9 5 10.3 Wind Load Analysis
  • 8. ∑V= 0 L1U1 = 0 L1L2 = L0L1 = 1.19k (C) ∑H= 0 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 2 2 L1L2 2-2 L0L1=1.19k L1U1 Wind Load Analysis
  • 9. 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 3 3 9 510.3 9 5 10.3 9 5 10.3 ∑ML0 = 0 – 0.23*6.86 + (5/10.3)*U1L2*6 + (9/10.3)*U1L2*(10/3)= 0 U1L2= 0.27 k (T) ∑V = 0 (9/10.3)*0.12+(9/10.3)*0.23 + (5/10.3)*U1U2 – (5/10.3)*0.27 – 2.60= 0 U1U2= 5.0 k (T) +ve 3-3 U1 L0 L1 L2 U2 0.23 k 0.12 k 2.60 k (10/3)’ 1.19k3.24k Wind Load Analysis
  • 10. 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 4 4 ∑H = 0 L2L3= 0.95 k (C) 5 9 10.3 L2L3 4-4 1.19k L2U2 0.27k ∑V = 0 L2U2 = (5/10.3)*0.27 L2U2= 0.13 k (C) L2L3 +1.19 – (9/10.3)*0.27 = 0 Wind Load Analysis
  • 11. 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 5 5 10 9 13.45 5 9 10.3 ∑ML0 = 0 (9/13.45)*U2L3*(20/3)+ (10/13.45)*U2L3*12 – 0.23*6.86 – 0.23*2*6.86 = 0 U2L3= 0.35 k (T) ∑V = 0 (5/10.3)*U2U3+ (9/10.3)*(0.12+0.23+0.23) – (10/13.45)*0.35 – 2.60 = 0 U2U3= 4.85 k (T) +ve 9 5 10.3 5-5 L0 L1 L2 L3 U1 U2 U3 0.12 k 2.60 k 0.23 k 0.95 k 2*(10/3) 0.23 k 3.24 k Wind Load Analysis
  • 12. (5/10.3)*U5L6+(9/10.3)*1.23 – 4.54 = 0 ∑V= 0 U5L6 = 7.14k (T) ∑H= 0 L5L6 = 5.64k (C) 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 6 6 5 9 10.3 5 9 10.3 4.54 k U5L6 1.23k 6-6 L5L6(5/10.3)*1.23 – (9/10.3)*7.14 – L5L6= 0 Wind Load Analysis
  • 13. 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 7 7 ∑H = 0 5.64k 7 – 7 L4L5 L5U5 ∑V = 0 L5U5= 0 L4L5 = 1.19k (C) Wind Load Analysis
  • 14. 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 8 8 5 9 10.3 9 510.3 9 5 10.3 L6 U5 L5L4 U4 2.46k 1.23k 4.54k 8-8 ∑ML6 = 0 2.46*6.86 – (5/10.3)*U5L4*6 – (9/10.3)*U5L4*(10/3)= 0 U5L4= 2.90 k (T) ∑V = 0 (9/10.3)*2.46+(9/10.3)*1.23 + (5/10.3)*U4U5 – (5/10.3)*2.90 – 4.54= 0 U4U5= 5.61 k (T) +ve Wind Load Analysis
  • 15. 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 9 9 ∑H = 0 L3L4= 3.11 k (C) ∑V = 0 L4U4 = (5/10.3)*2.90 L4U4= 1.41 k (C) L3L4+ (9/10.3)*2.90 – 5.64 = 0 9 510.3 5.64k 9-9 L4U4 2.90k L3U4 Wind Load Analysis
  • 16. 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 10 10 9 5 10.3 9 10 13.45 9 5 10.3 2.46k 2.46k 1.23k 4.54k L6L5L4L3 U3 U5 U4 3.11k 10 -10∑ML6 = 0 –(9/13.45)*U4L3*(20/3) – (10/13.45)*U4L3*12 + 2.46*6.86 +2.46*2*6.86 = 0 U4L3= 3.78 k (T) ∑V = 0 (5/10.3)*U3U4 + (9/10.3)*(1.23+2*2.46) – (10/13.45)*3.78 – 4.54 = 0 U3U4= 4.07 k (T) +ve Wind Load Analysis
  • 17. 6@6 ft = 36 ft 10 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 R1 R2 H 3@6.86 ft 0.23k 0.23k 0.12k 0.12k 2.46k 2.46k 1.23k 1.23k 5 9 10.3 9 5 10.3 = 3.24k = 4.54k = 2.60k 11 11 ∑V = 0 9 10 13.45 9 10 13.45 3.11k 11 – 11 0.95k L3U3 L3 0.35k 3.78k(10/13.45)*3.78 + (10/13.45)*0.35 – L3U3= 0 L3U3= 3.07 k (C) Wind Load Analysis
  • 18. (- 1.19) (-1.19) (-0.95) (-3.11) (-5.64) (-5.64) (5.14) (5.00) (4.85) (4.07) (5.61) (7.14) 6@6 ft = 36 ft L0 L1 L2 L3 L4 L5 L6 U1 U2 U3 U4 U5 4.54 k2.60 k (0) (-0.13) (-1.41) (0) (-3.07) (0.35) (0.27) (3.78) (2.90) 3.24k L R Wind Load Analysis