Week 12 - Recap For Mid Term
Week 12 - Recap For Mid Term
Week 12 - Recap For Mid Term
❖ The relationship between stress and strain in concrete can be described by the stress-strain curve, which
illustrates how the material responds to applied loads. The stress-strain curve for concrete typically exhibits
several distinct phases:
1. Elastic Phase: In the initial stage, when the applied stress is within the elastic limit of the concrete, the material behaves
elastically. This means that the stress and strain are proportional, and upon the removal of the load, the
concrete will return to its original shape with no permanent deformation.
2. Yielding : It refers to the point at which a material undergoes significant deformation without an increase in stress.
It is a characteristic behavior observed in ductile materials, such as metals and some types of alloys.
3. Strain Hardening : Following yielding, concrete can exhibit strain hardening behavior, particularly when it contains
reinforcing steel bars. This phase involves an increase in stress with increasing strain, indicating that the
concrete becomes stronger and can carry higher loads.
4. Ultimate Failure: Refer to the point at which a material or structure can no longer sustain the applied loads and undergoes
complete failure.
Relationship of stress-strain for concrete with aid of diagram
Chapter 2 – Design for flexure
Two different types of problems arise in the study of reinforced concrete flexural elements:
1. Design : Given a cross section, concrete strength, steel reinforcement strength, and applied ultimate
bending moment, determine the area and number of reinforcement required.
2. Design check : Given a cross section, concrete strength, number, strength and size of steel reinforcement
provided, determine the moment of resistance.
A rectangular reinforced concrete beam has to support a design moment of 230 kNm. Solve the area
of reinforcement required if the beam dimension is 350 (b) x 550 mm (d), concrete strength, fck =
25 N/mm² and steel strength, fyk = 500 N/mm.
Specification :
Beam size b x d = 350 x 550 mm
Chac. Strength of concrete, fck = 25 N/mm²
Chac. Strength of steel, fyk = 500 N/mm²
Bending moment, M = 175 kNm
Step 2: Determine the area of reinforced steel bar required
Lever arm , Z
Z = d – 0.4x
= 550 – (0.4 x 138.7)
= 494.5 mm < 0.95d = 522.5 mm (so take the smallest for z)
Area of tension reinforcement , As
As = M / 0.87 fyk . z
= 175 x 10⁶ / (0.87 X 500 X 494.5)
= 813.5 mm
650 mm
Overall depth, h = L/13 = 8000/13 = 615 mm
Width, b = 0.4 h = 0.4 x 615 = 246 mm
From Table 5.4, see at R60, 𝑏𝑚𝑖𝑛 for this case is 300 mm
(see slide no. 9), so a = 25 mm from Table 5.4 (refer next slide)
Chapter 2 – Simply Support Rectangular Beam Design
(cont’d)
Chapter 2 – Simply Support Rectangular Beam Design
(cont’d)
Effective depth,
d = h - 𝐶𝑛𝑜𝑚 - ∅ 𝑙𝑖𝑛𝑘 − ∅bar/2 = 650 – 30 – 8 – (20/2) = 602 mm
Concrete strut capacity, 𝑉𝑅𝑑,𝑚𝑎𝑥 = [0.36 𝑏𝑤 d𝑓𝑐𝑘 (1-𝑓𝑐𝑘 /250)]/(cot 𝜃 + tan 𝜃) cot 22° = 1/tan22°=2.5
tan 22° = 0.4
Try for cot 22°
= [[(0.36 x 250 x 602 x 30 x ( 1-30/250)]/(cot 22° + tan 22°)]/1000 (for conversion unit to kN)
= 493.2 kN > 𝑽𝑬𝒅 =167.6 kN
Cot 22°
Try link: H6, 𝐴𝑠𝑤 = 57 mm² (From table A, assume for 2 rebar H6)
167.6 x 103 Spacing, s = 57/0.28
= s = 203.5 mm ~ 204 mm
0.78 x 500 x 602 x 2.5
= 0.28
Chapter 2 – Simply Support Rectangular Beam Design
(cont’d)
Therefore, S=204 mm < S max -------- Hence, take bar spacing = 225 mm Use H6-225 c/c
Therefore, S=259 mm < S max =487.5 -------- Hence, take bar spacing = 300 mm (at middle) Use H6-300 c/c
X=1.03m
124.4 kN
167.6 kN
H6-225 H6-300 H6-225
1.03m 5.94m 1.03m