CE 415 Design of steel structures

CE 318

STRUCTURE ANALYSIS AND DESIGN II LAB

LECTURE 4

BEAM LOAD CALCULATION

COURSE TEACHER: SAURAV BARUA CONTACT NO: +8801715334075

EMAIL: saurav.ce@diu.edu.bd

LECTURE PLAN

Stair load calculation

Moment calculation

Reinforcement calculation

Stair reinforcement detailing

BEAM LAYOUT

BEAM CONTRIBUTORY AREA

CONTRIBUTORY AREA

• Beam B1 size = 12”x 18” (assume) explain in the class!!

• B1 contributory area = 2 x ½ x 15 x 4 + ½ x (9+18) x 8

= 168 sq. ft explanation Dead load calculation:

Slab thickness = 5”

Floor finish (FF) = 25 psf Wall load = 80 psf

B1 length = 15+18+ 15 = 48 ft.

CONTRIBUTORY AREA

• Dead load on beam = 5/12 x 0.15 + 0.025 + 0.08 ≈ 0.17 ksf x 168 = 286 kip / 48 = 5.96k/ft

Self weight of beam = (12 x 18)/(12 x 12) x 0.15 = 0.23 k/ft Total DL on beam per ft = 5.96+0.23 = 6.19 k/ft

Live load = 40 psf (BNBC)

Live load (LL) per ft = 0.04 x 168 = 6.72 kip /48 = 0.14k/ft

DEAD LOAD MOMENT (DLM)

M

_DL

,

_A-ve

= - 1/16 x w x L

²

= -1/16 x 6.19 x 15

²

= -87.1 k-ft/ft M

_DL

,

_B+ve

= + 1/14 x w x L

²

= +1/14 x 6.19 x 15

²

= +99.5 k-ft/ft M

_DL

,

_C-ve

=- 1/11 x w x L

²

= -1/11 x 6.19 x 18

²

= -182.32 k-ft/ft (Explanation!!)

M

_DL

,

_D+ve

=+ 1/14 x w x L

²

= -1/14 x 6.19 x 18

²

= +143.25 k-ft/ft

LIVE LOAD MOMENT (LLM)

M

_LL

,

_A-ve

= - 1/16 x w x L

²

= -1/16 x 0.14 x 15

²

= -1.97 k-ft/ft M

_LL

,

_B+ve

= + 1/14 x w x L

²

= +1/14 x 0.14 x 15

²

= +2.25 k-ft/ft M

_LL

,

_C-ve

=- 1/11 x w x L

²

= -1/11 x 0.14 x 18

²

= -4.12 k-ft/ft (Explanation!!)

M

_LL

,

_D+ve

=+ 1/14 x w x L

²

= -1/14 x 0.14 x 18

²

= +3.24 k-ft/ft

DEAD LOAD SHEAR (DLV)

V

_DL

,

_A+ve

= + 1/2 x w x L = +1/2 x 6.19x 15 = +46.43k/ft

V

_DL

,

_C-ve

= - 1/2 x w x L = -1/2 x 6.19 x 18 = -55.71 k-ft/ft

Take maximum shear. Shear +ve/-ve does not matter!!

LIVE LOAD SHEAR (LLV)

V

_LL

,

_A+ve

= + 1/2 x w x L = +1/2 x 0.14x 15 = +1.05 k-ft/ft

V

_LL

,

_C-ve

= - 1/2 x w x L = -1/2 x 0.14 x 18 = -1.26 k-ft/ft

Take maximum shear. Shear +ve/-ve does not matter!!

• Thumb rule,

• Earthquake load (EQ) = 10% of DL

• Wind load (WL) = 15% of DL

EARTHQUAKE LOAD MOMENT (EQM)

M

_EQ

,

_A-ve

= 0.1 x 87.1 = +8.7 k-ft/ft M

_EQ

,

_B+ve

= 0

M

_EQ

,

_C-ve

= 0.1 x 182.32 = -18.23 k-ft/ft

M

_EQ

,

_D+ve

= 0

WIND LOAD MOMENT (WLM)

M

_wL

,

_A-ve

= 0.15 x 87.1 = 13.07 k-ft/ft M

_wL

,

_B+ve

= 0

M

_wL

,

_C-ve

= 0.15 x 182.32 = 27.35 k-ft/ft

M

_wL

,

_D+ve

= 0

EARTHQUAKE LOAD SHEAR (EQV)

V

_EQ

,

_A-ve

= 0.1 x 46.43 = 4.7 k/ft V

_EQ

,

_B+ve

= 4.7k/ft

V

_EQ

,

_C-ve

= 0.1 x 55.71 = 5.6 k/ft

V

_EQ

,

_D+ve

= 5.6 k/ft

WIND LOAD SHEAR (WLV)

V

_WL

,

_A-ve

= 0.15 x 46.43 = 6.96 k/ft V

_WL

,

_B+ve

= 6.96k/ft

V

_WL

,

_C-ve

= 0.15 x 55.71 = 8.36 k/ft

V

_WL

,

_D+ve

= 8.36 k/ft

LOAD COMBINATION

• There are 16 load combination as per BNBC for buildings, in total 26 load

combinations. We will consider main 4 combination here. (Explanation in class!!) 1. 1.4 DL + 1.7 LL

2. 1.05 DL + 1.05 LL + 1.275 WL 3. 1.05 DL + 1.05 LL + 1.403 EQ 4. 1.4 DL + 1.4 LL + 1.4 EQ

EQ can be EQX+, EQX-, EQY+, EQY- WL can be WLX+, WLX-, WLY+, WLY-

MOMENT (k-ft/ft)

A B C D

DLM -87.1 +99.5 -182.32 +143.25

LLM -1.97 +2.25 -4.12 +3.24

EQM +8.7 0 -18.23 0

WLM +8.7 0 -18.23 0

SHEAR (k/ft)

A B C D

DLV +46.43 0 -55.71 0

LLV -1.05 0 -1.26 0

EQV +4.7 +4.7 +5.6 +5.6

WLV +6.96 +6.96 +8.36 +8.36

COMBINATION OF MOMENT (k-ft/ft)

Load combo

A B C D

1 -125.29 143.13 -262.25 206.06 2 -82.43 106.84 -219.01 153.81 3 -81.32 106.84 -221.34 153.81

COMBINATION OF SHEAR (k/ft)

copyright @Saurav Barua

Load

combo A B C D

1 63.22 0.00 -

80.14 0.00 2 56.52 8.87 -

49.16 10.66 3 54.24 6.59 -

51.96 7.86 4 70.11 6.58 -

71.92 7.84