Homework

V V V V V V V

BEAM section g1 g2 0,3 q check stirrusp Vrd check

ED ED mi n ma x mi n ma x ed,ma x,a s s

end1 85,60 -1,24 82,52 161,80 20,05 20,28 3,00 9,98 120,01 -42,87 172,87 0,08 -0,25 ok ok 172,87 3ϕ8/100 196,49 ok

P15-P16 mid -0,19 -32,52 161,80 82,52 20,05 20,28 3,00 32,52 3ϕ8/150 131,00 ok

end2 -75,83 -154,61 82,52 161,80 20,05 20,28 3,00 9,98 120,01 -42,87 172,87 0,08 -0,25 ok ok 172,87 3ϕ8/100 196,49 ok

end1 -75,83 -154,61 82,52 161,80 20,05 20,28 3,00 75,32 141,34 43,61 173,05 0,53 0,25 ok ok 173,05 3ϕ8/100 196,49 ok

P16-P17 mid 5,17 -10,97 161,80 82,52 20,05 20,28 3,00 10,97 3ϕ8/150 131,00 ok

end2 -57,38 -182,54 82,52 161,80 20,05 20,28 3,00 75,32 141,34 43,61 173,05 0,53 0,25 ok ok 182,54 3ϕ8/100 196,49 ok

end1 -57,38 -182,54 82,52 161,80 19,40 18,04 4,50 7,90 117,93 -44,96 170,78 0,07 -0,26 ok ok 182,54 3ϕ8/100 196,49 ok

P17-P18 mid 37,40 -23,67 161,80 82,52 19,40 18,04 4,50 37,40 3ϕ8/150 131,00 ok

end2 -9,31 -143,32 82,52 161,80 19,40 18,04 4,50 7,90 117,93 -44,96 170,78 0,07 -0,26 ok ok 170,78 3ϕ8/100 196,49 ok

end1 -9,31 -143,32 82,52 161,80 20,05 20,28 3,00 75,32 141,34 43,61 173,05 0,53 0,25 ok ok 173,05 3ϕ8/100 196,49 ok

P18-P19 mid 10,98 -3,63 161,80 82,52 20,05 20,28 3,00 10,98 3ϕ8/150 131,00 ok

end2 -64,96 -186,60 82,52 161,80 20,05 20,28 3,00 75,32 141,34 43,61 173,05 0,53 0,25 ok ok 186,60 3ϕ8/100 196,49 ok

end1 -64,96 -186,60 82,52 161,80 21,07 10,14 1,50 -5,95 104,08 -58,80 156,93 -0,06 -0,37 ok ok 186,60 3ϕ8/100 196,49 ok

P19-P6 mid 32,33 3,18 161,80 82,52 21,07 10,14 1,50 32,33 3ϕ8/150 131,00 ok

end2 -0,53 -56,94 82,52 161,80 21,07 10,14 1,50 -5,95 104,08 -58,80 156,93 -0,06 -0,37 ok ok 156,93 3ϕ8/100 196,49 ok

V stirrusp Vrd check

BEAM section ed,ma x,a s s

172,87 3ϕ8/100 196,49 ok

end1 32,52 3ϕ8/150 131,00 ok

P15-P16 mid 172,87 3ϕ8/100 196,49 ok

end2 173,05 3ϕ8/100 196,49 ok

end1 10,97 3ϕ8/150 131,00 ok

P16-P17 mid 182,54 3ϕ8/100 196,49 ok

end2 182,54 3ϕ8/100 196,49 ok

end1 37,40 3ϕ8/150 131,00 ok

P17-P18 mid 170,78 3ϕ8/100 196,49 ok

end2 173,05 3ϕ8/100 196,49 ok

end1 10,98 3ϕ8/150 131,00 ok

P18-P19 mid 186,60 3ϕ8/100 196,49 ok

end2 186,60 3ϕ8/100 196,49 ok

end1 32,33 3ϕ8/150 131,00 ok

P19-P6 mid 156,93 3ϕ8/100 196,49 ok

end2

Figure 6.15: Shear resistance verification

6.2.3 Ductility check

The critical zone is the distance between the extremity where column and beam intersect, and it

= ℎ

.

is equal to = 0.40

b

According to NTC, chapter 7.4.4.1.2 the ductility demand is expressed through the ductility factor

μ that can be computed as follow:

ϕ

Where T is the fundamental period, equal to 0.3178 s.

1

Minimum and maximum amount of longitudinal reinforcement is required:

1.4 3.5

< < +

–

38 EARTHQUAKE RESISTANT DESIGN A.Y. 2023-24 Prof. Chesi & Martinelli

ℎ , where ℎc

The diameter of the longitudinal bars should be not greater than is the height of

c

the column.

Where:

• is the normalised design axial force in the column, taken with its minimum value for

ν

d

the seismic design situation.

• is 2/3 for DCM.

K D

• is equal for 1 for DCM.

γ

Rd

Finally, the computed maximum diameter was 20mm > 16mm.

Regarding the longitudinal step of the stirrups in the critical zone, NTC requires a maximum

value equal to: ℎ

= min ; 24 ; 225 ; 8 = 100

{ }

4

"check ductility al positivo" "check ductility al negativo"

ρ ρ ρ ρ

ρ ρ'

BEAM ρ'/ρ verifiche + ρ

section ρ' ρ'/ρ verifiche +

mi n ma x mi n ma x

0,01005 0,00503 0,003111 0,01280 0,5 ok ok ok 0,00503

end1 0,01005 0,00311 0,01783 2 ok ok ok

P15-P16 0,01005 0,00503 0,003111 0,01280 0,5 ok ok ok 0,00503

mid 0,01005 0,00311 0,01783 2 ok ok ok

0,01005 0,00503 0,003111 0,01280 0,5 ok ok ok 0,00503

end2 0,01005 0,00311 0,01783 2 ok ok ok

0,01005 0,00503 0,003111 0,01280 0,5 ok ok ok 0,00503

end1 0,01005 0,00311 0,01783 2 ok ok ok

P16-P17 0,01005 0,00503 0,003111 0,01280 0,5 ok ok ok 0,00503

mid 0,01005 0,00311 0,01783 2 ok ok ok

0,01005 0,00503 0,003111 0,01280 0,5 ok ok ok 0,00503

end2 0,01005 0,00311 0,01783 2 ok ok ok

0,01005 0,00503 0,003111 0,01280 0,5 ok ok ok 0,00503

end1 0,01005 0,00311 0,01783 2 ok ok ok

0,01005 0,00503

P17-P18 0,003111 0,01280 0,5 ok ok ok 0,00503

mid 0,01005 0,00311 0,01783 2 ok ok ok

0,01005 0,00503 0,003111 0,01280 0,5 ok ok ok 0,00503

end2 0,01005 0,00311 0,01783 2 ok ok ok

0,01005 0,00503 0,00311 0,01280 0,5 ok ok ok 0,00503

end1 0,01005 0,00311 0,01783 2 ok ok ok

0,01005 0,00503

P18-P19 0,00311 0,01280 0,5 ok ok ok 0,00503

mid 0,01005 0,00311 0,01783 2 ok ok ok

0,01005 0,00503 0,00311 0,01280 0,5 ok ok ok 0,00503

end2 0,01005 0,00311 0,01783 2 ok ok ok

0,01005 0,00503 0,00311 0,01280 0,5 ok ok ok 0,00503

end1 0,01005 0,00311 0,01783 2 ok ok ok

0,01005 0,00503

P19-P6 0,00311 0,01280 0,5 ok ok ok 0,00503

mid 0,01005 0,00311 0,01783 2 ok ok ok

0,01005 0,00503 0,00311 0,01280 0,5 ok ok ok 0,00503

end2 0,01005 0,00311 0,01783 2 ok ok ok

Figure 6.16: Ductility check 39

6.3 Secondary beam

Secondary beams are arranged parallel to the floors, connecting the pillars of the same structural

axis to each other, and unlike the primary beams they do not carry any load except their own

weight, in fact they have the main function of promoting the frame functioning of the entire build-

ing.

Like primary beams they have 30 cm x40 cm rectangular cross-sections.

The procedure followed is the same of primary beams, so for the sake of an easier reading it will

report only the results.

6.3.1 Bending resistance

-40

-30

-20

-10 0 2 4 6 8 10 12 14 16

0

10

20

30 Figure 6.17: Bending moment envelope

• At support

ϕ16 ϕ16

It was chosen 2 and 2 respectively for tensile and compressed reinforcement.

Table 6.9: Support

Parameter Value UoM

-26.64 kNm

-55.76 kNm

2

204.48

2

185.76

, 2

4800.00

, 2

402.12

, 2

′

402.12

, –

40 EARTHQUAKE RESISTANT DESIGN A.Y. 2023-24 Prof. Chesi & Martinelli

• At midspan

ϕ16 ϕ16

It was chosen 2 and 2 respectively for tensile and compressed reinforcement.

Table 6.10: Midspan

• Parameter Value UoM

26.64 kNm

55.76 kNm

2

204.48

2

185.76

, 2

4800.00

, 2

402.12

, 2

′

402.12

,

SLU SLV check bending moment

+ + - + - + -

M M M M M M M

BEAM section bars at bottom bars at top Mrd > Med

ED ED ED ED ED rd rd

end1 0,00 -18,78 6,46 -29,85 6,46 -29,85 2ϕ16 2ϕ16 55,76 55,76 ok ok

P12-P11 mid 26,51 4,707 3,48 3,09 26,51 3,09 2ϕ16 2ϕ16 55,76 55,76 ok ok

end2 -16,48 -31,62 17,61 -18,58 17,61 -31,62 2ϕ16 2ϕ16 55,76 55,76 ok ok

end1 -16,48 -31,62 8,56 -22,52 8,56 -31,62 2ϕ16 2ϕ16 55,76 55,76 ok ok

P10-P9 mid 16,18 -6,50 3,21 2,98 16,18 -6,50 2ϕ16 2ϕ16 55,76 55,76 ok ok

end2 -16,48 -31,62 10,01 -21,16 10,01 -31,62 2ϕ16 2ϕ16 55,76 55,76 ok ok

end1 -16,48 -31,62 16,34 -20,03 16,34 -31,62 2ϕ16 2ϕ16 55,76 55,76 ok ok

P9-P8 mid 26,64 4,26 3,36 2,99 26,64 2,99 2ϕ16 2ϕ16 55,76 55,76 ok ok

end2 0,00 -18,78 7,65 -28,74 7,65 -28,74 2ϕ16 2ϕ16 55,76 55,76 ok ok

Figure 6.18: Bending resistance verification

-40

-30

-20

-10

0,00 2,00 4,00 6,00 8,00 10,00 12,00 14,00 16,00

0

10

20 Figure 6.19: Bending moment envelope due to seismic combination 41

6.3.2 Shear resistance

-40

-30

-20

-10 0 2 4 6 8 10 12 14 16

0

10

20

30

40 Figure 6.20: Shear envelope

• At support

Stirrups= ϕ8/100 Table 6.11: Support

Parameter Value UoM

45 °

0.6 -

333 2

100.53

100

1018.9 kN

131.0 kN

131.0 kN

• At midspan

Stirrups= ϕ8/200 Table 6.12: Midspan

Parameter Value UoM

45 °

0.6 -

333 2

100.53

200

1018.9 kN

65.5 kN

65.5 kN

–

42 EARTHQUAKE RESISTANT DESIGN A.Y. 2023-24 Prof. Chesi & Martinelli

SLU Calcolo seismic shear according to EC8 5.4.2.2 + -

ζ ζ

+ -

+ - + x+ - x-

Mid Mid

V V V V V V V

BEAM section g1 g2 0,3 q check stirrusp Vrd check

ED ED mi n ma mi n ma ed,ma x,a s s

end1 125,25 93,94 82,52 161,80 21,07 10,14 1,5 48,76 114,78 17,05 146,49 0,42 0,12 ok ok 146,49 3ϕ8/100 196,49 ok

P12-P11 mid 30,06 -36,32 161,80 55,74 21,07 10,14 1,5 17,05 146,49 59,48 104,07 146,49 3ϕ8/200 98,25

end2 -125,25 -156,56 82,52 82,52 21,07 10,14 1,5 48,76 114,78 48,76 114,78 0,42 0,42 ok ok 156,56 3ϕ8/100 196,49 ok

end1 135,06 68,57 82,52 161,80 21,07 10,14 1,5 48,76 114,78 17,05 146,49 0,42 0,12 ok ok 146,49 3ϕ8/100 196,49 ok

P10-P9 mid -0,21 -5,38 82,54 82,54 21,07 10,14 1,5 48,76 114,79 48,76 114,79 114,79 3ϕ8/200 98,25

end2 -68,38 -118,85 82,52 161,80 21,07 10,14 1,5 48,76 114,78 17,05 146,49 0,42 0,12 ok ok 146,49 3ϕ8/100 196,49 ok

end1 -68,38 -118,85 82,52 161,80 21,07 10,14 1,5 -5,95 104,08 -58,80 156,93 -0,06 -0,37 ok ok 156,93 3ϕ8/100 196,49 ok

P9-P8 mid 12,94 -1,12 82,54 82,54 21,07 10,14 1,5 -5,97 104,09 -5,97 104,09 104,09 3ϕ8/200 98,25

end2 -17,19 -56,23 82,52 161,80 21,07 10,14 1,5 -5,95 104,08 -58,80 156,93 -0,06 -0,37 ok ok 156,93 3ϕ8/100 196,49 ok

V

BEAM stirrusp Vrd

section check

ed,ma x,a s s

46.70 ϕ8/100 131.00

end1 ok

46.70

P12-P11 ϕ8/200

mid 65.50

46.70 ϕ8/100 131.00

end2 ok

46.70 ϕ8/100 131.00

end1 ok

46.70

P10-P9 ϕ8/200

mid 65.50

46.70 ϕ8/100 131.00

end2 ok

46.70 ϕ8/100 131.00

end1 ok

46.70

P9-P8 ϕ8/200

mid 65.50

46.70 ϕ8/100 131.00

end2 ok

Figure 6.21: Shear resistance verification

20

10

0

0,00 2,00 4,00 6,00 8,00 10,00 12,00 14,00 16,00

-10

-20 Figure 6.22: Shear envelope due to seismic combination 43

6.3.3 Ductility check "check ductility al positivo" "check ductility al negativo"

ρ ρ ρ ρ

BEAM section ρ ρ' ρ'/