Reinforced Concrete II Hashemite University The Hashem ite University Departm ent of Civil Engineering Lecture 3.3 – Lecture 3.3 – Shear Strength Shear Strength of Slabs of Slabs Dr. Hazim Dwairi Dr Hazim Dwairi Dr Hazim Dwairi Dr. Hazim Dwairi Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Shea r Strength of Sla bs Shea r Strength of Sla bs • In two In two- -way floor systems, the slab must way floor systems, the slab must have adequate thickness to resist both have adequate thickness to resist both h h d d t t thi k thi k t t i t b th i t b th bending moments and shear forces at bending moments and shear forces at critical section. There are three cases to critical section. There are three cases to look at for shear. look at for shear. – One One- -way Slabs supported on beams way Slabs supported on beams – Two Two- -Way Slabs without beams Way Slabs without beams – Shear Reinforcement in two Shear Reinforcement in two- -way slabs without way slabs without beams. beams. The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Dr. Hazim Dwairi Dr. Hazim Dwairi Dr. Hazim Dwairi 1
Reinforced Concrete II Hashemite University One One- -w a y Shea r: Sla bs w ith w a y Shea r: Sla bs w ith Bea m s Bea m s Two Two- -way slabs supported on beams (one way slabs supported on beams (one- -way way shear): shear): shear): shear): The critical section for shear is found at d distance The critical section for shear is found at distance from the column, where: from the column, where: ⎛ ⎞ ' f ⎜ ⎟ φ = φ c V bd ⎜ ⎜ ⎟ ⎟ c ⎝ 6 6 ⎝ ⎠ ⎠ The supporting beams are stiff and are capable of The supporting beams are stiff and are capable of transmitting floor loads to the columns. transmitting floor loads to the columns. The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Dr. Hazim Dwairi Dr. Hazim Dwairi One One- -w a y Shea r: Sla bs w ith w a y Shea r: Sla bs w ith Bea m s Bea m s The ultimate shear force is calculated using the triangular and The ultimate shear force is calculated using the triangular and t ape o da a eas t ape o da a eas trapezoidal areas. If no shear reinforcement is provided, the trapezoidal areas. If no shear reinforcement is provided, the o s ea o s ea e e o ce o ce e t s p o ded, t e e t s p o ded, t e shear force at a distance d from the beam must be: shear force at a distance from the beam must be: ≤ φ V V u@d c Where: Where: ⎛ ⎞ l = − ⎜ ⎟ 2 V w d u@d u ⎝ ⎠ 2 The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Dr. Hazim Dwairi Dr. Hazim Dwairi Dr. Hazim Dwairi 2
Reinforced Concrete II Hashemite University Shea r in Sla bs w ithout Bea m s Shea r in Sla bs w ithout Bea m s • There are two types of shear that need to be There are two types of shear that need to be addressed addressed addressed addressed way shear or beam shear at distance d from the – One One- -way shear or beam shear at distance from the column column – Two Two- -way or punch out shear which occurs along a way or punch out shear which occurs along a truncated cone. truncated cone. Two-way shear One-way shear The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Dr. Hazim Dwairi Dr. Hazim Dwairi One One- -w a y shea r (Bea m Shea r) w a y shea r (Bea m Shea r) One- One -way shear considers critical section a way shear considers critical section a distance d from the column and the slab is d f distance di t di t from the column and the slab is f th th l l d th d th l b i l b i considered as a wide beam spanning considered as a wide beam spanning between supports. between supports. ⎛ ⎞ ' f ⎜ ⎜ ⎟ ⎟ ≤ ≤ φ φ = φ φ c V V V V bd bd ⎜ ⎟ u@d c 6 ⎝ ⎠ The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Dr. Hazim Dwairi Dr. Hazim Dwairi Dr. Hazim Dwairi 3
Reinforced Concrete II Hashemite University Tw o Tw o- -w a y Shea r: Critica l Section w a y Shea r: Critica l Section Two- Two -way shear fails along a truncated cone or way shear fails along a truncated cone or pyramid around the column. The critical section is pyramid around the column pyramid around the column pyramid around the column. The critical section is The critical section is The critical section is located d/2 d/2 from the column face, column capital, located from the column face, column capital, or drop panel. or drop panel. The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Dr. Hazim Dwairi Dr. Hazim Dwairi Tw o Tw o- -w a y Shea r: Critica l Section w a y Shea r: Critica l Section The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Dr. Hazim Dwairi Dr. Hazim Dwairi Dr. Hazim Dwairi 4
Reinforced Concrete II Hashemite University Tw o Tw o- -w a y Shea r: Concrete Shea r w a y Shea r: Concrete Shea r Strength Strength • For Slabs and footings, For Slabs and footings, V c is the smallest of a, b is the smallest of a, b and c: and c: and c: and c: Where: b o = perimeter of critical section β = ratio of long side of column to short side α s = 40 for interior columns, 30 for edge columns and 20 for corner columns. The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Dr. Hazim Dwairi Dr. Hazim Dwairi w a y Shea r: β Ev a lua tion Tw o Tw o- -w a y Shea r: Ev a lua tion The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Dr. Hazim Dwairi Dr. Hazim Dwairi Dr. Hazim Dwairi 5
Reinforced Concrete II Hashemite University Augm enting Shea r Strength Augm enting Shea r Strength • For slabs which don’t meet the condition for For slabs which don’t meet the condition for shear, one can either: shear one can either: shear one can either: shear, one can either: – Thicken the slab over the entire panel. Thicken the slab over the entire panel. – Use a drop panel to thicken the slab adjacent to the Use a drop panel to thicken the slab adjacent to the column. column. Increase b o by increasing the column size, or by – Increase by increasing the column size, or by adding a fillet or shear capital around the column. adding a fillet or shear capital around the column. – Add shear reinforcement. Add shear reinforcement. Reinforcement can be done by shear heads, anchor bars, Reinforcement can be done by shear heads, anchor bars, conventional stirrup cages and studded steel strips. conventional stirrup cages and studded steel strips. The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Dr. Hazim Dwairi Dr. Hazim Dwairi Shea r Reinforcem ent Shea r Reinforcem ent • Shear Shear- -heads heads : consist of steel I : consist of steel I- -beams or channel beams or channel welded into four cross arms to be placed in slab above a welded into four cross arms to be placed in slab above a column. Does not apply to external columns due to column column column. Does not apply to external columns due to Does not apply to external columns due to Does not apply to external columns due to lateral loads and torsion. lateral loads and torsion. The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Dr. Hazim Dwairi Dr. Hazim Dwairi Dr. Hazim Dwairi 6
Reinforced Concrete II Hashemite University Shea r Reinforcem ent Shea r Reinforcem ent • Anchor Bars Anchor Bars : consists of steel reinforcement rods or : consists of steel reinforcement rods or bent bar reinforcement . bent bar reinforcement . bent bar reinforcement . bent bar reinforcement . The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Dr. Hazim Dwairi Dr. Hazim Dwairi Shea r Reinforcem ent Shea r Reinforcem ent • Conventional Stirrup Cages Conventional Stirrup Cages : h ≥ 150 mm h ≥ 16d s h = The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Dr. Hazim Dwairi Dr. Hazim Dwairi Dr. Hazim Dwairi 7
Reinforced Concrete II Hashemite University Shea r Reinforcem ent Shea r Reinforcem ent • Headed Shear Studs Headed Shear Studs : The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Dr. Hazim Dwairi Dr. Hazim Dwairi Nom ina l Shea r Strength Nom ina l Shea r Strength • Shear reinforcement consisting of bars or wires Shear reinforcement consisting of bars or wires and single and single- - or multiple or multiple- -leg stirrups shall be leg stirrups shall be permitted in slabs and footings where h is permitted in slabs and footings where h is itt d i itt d i l b l b d f d f ti ti h h h i h i greater than or equal to 150mm & 16d greater than or equal to 150mm & 16d s Conventional = + ≤ ' V V V 0 . 5 f b d Stirrup Cage n c s o c = + ≤ Shear Head ' V V V 0 . 58 f f c b d Reinforcement Reinforcement n n c c s s c o o ≤ ' V 0 . 17 f b d c c o A f d = v y V s S The Hashemite University The Hashemite University Reinforced Concrete II Reinforced Concrete II Dr. Hazim Dwairi Dr. Hazim Dwairi Dr. Hazim Dwairi 8
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