Report: Testing of a Beam in Pure Shear

DESIGN OF RCC STRUCTURES (ENCE 352)

Report: Testing of a Beam in Pure Shear

1. Objective of Testing a Beam in Pure Shear

i. To know about the modes of shear failure in a reinforced concrete (RC) beam.

2. Theory: Understanding a Beam in Pure Shear

Shear force is present in a beam where there is a change in bending moment along the span. It is equal to the rate of change of bending moment. Several experimental analyses of shear in concrete beams are quite complex, but they have been conducted to understand the various modes of failure which could occur due to a possible combination of shear and bending moment acting at a given section.

Modes of Failure

The primary modes of shear failure in concrete are:

Diagonal tension failure
Diagonal shear failure
Diagonal compression failure

Studies have shown that the shear force is resisted by the uncracked concrete in the compression region, the aggregate interlocking, and the shear acting across the longitudinal steel bars. Shear reinforcement, if present, will also significantly resist shear failure.

3. Materials and Equipment

Materials Required

i. RC Beam of span 700 mm
ii. M20 concrete
iii. Fe500 with shear reinforcement

Equipment

Beam Testing Machine (UTM/CTM setup)

4. Procedures

The formwork was cleaned, prepared, and greased.
Longitudinal bars and 2-8 mm φ bars were cut to a length of 800 mm and edges were bent up to 850 mm in each.
2-8 mm φ bars were placed at the lower side and 2-8 mm φ bars were placed at the top.
3-6 mm φ bars were used for vertical stirrups.
The concrete mix was prepared from the calculated amount of cement, sand, aggregates, and water in a given proportion.
The steel framework was placed inside the formwork and was filled by concrete mix by pouring and compacting, and then allowed to settle for 24 hours.
Three cubes of size 150 mm × 150 mm × 150 mm were also cast simultaneously.
After 24 hours, the formwork was removed, and the specimens were cured for 28 days before testing was performed on them.

5. Experimental Observations and Calculations

Concrete Cube Test — Fig 1: Concrete Cube Compression Test

Pure Shear Test Setup of a Beam — Fig 2: Beam Pure Shear Test Setup

5.1 Concrete Cubes Test Data (28 Days)

Test Period	Cube No.	Weight (kg)	Failure Load (kN)	Compressive Strength (MPa)
28 Days	1	8.235	643.2	28.58
	2	8.415	444.8	19.76
	3	8.200	666.2	29.60
	Mean	–	584.73	25.98

5.2 Beam Pure Shear Test Data

Beam No.	Crack Width	First Crack Load (kN)	Failure Load (kN)
1	4 mm	35.6	105.4

5.3 Calculations

Section Properties:

Dimension of Beam: 700 mm × 150 mm × 150 mm
Effective depth (d): 150 – 25 – 4 – 6 = 115 mm
Dead load (w): 0.15 × 0.15 × 0.5 × 25 = 0.5625 kN/m
Spacing of stirrups (s_v): 300 mm

Material Properties:

Area of tensile steel (A_st): (2 × π × 8²) / 4 = 100.53 mm²
Area of vertical steel (A_sv): (2 × π × 6²) / 4 = 56.55 mm²
Grade of steel: Fe500 (tensile), Fe250 (stirrups)
Grade of concrete: M20

Percentage of Tensile Steel (p_t):

p_t = \frac{A_{st}}{bd} \times 100\% = \frac{100.53}{150 \times 115} \times 100\% = 0.58\%

Design Shear Strength (τ_c) from Table 19 of IS 456:2000:

p_t (%)	τ_c (N/mm²)
0.50	0.48
0.58	τ_c (Interpolated) = 0.505
0.75	0.51

Note: Maximum shear strength, τ_c,max = 2.8 N/mm².

Shear Capacity Computations:

1. Permissible Shear Force by Concrete (V_c):

V_c = \tau_c \times b \times d = 0.505 \times 150 \times 115 = 8.722\text{ kN}

2. Increment in Shear Resistance Due to Stirrups (V_us):

V_{us} = \frac{0.87 f_y A_{sv} d}{s_v} = \frac{0.87 \times 250 \times 56.55 \times 115}{300} = 4.714\text{ kN}

3. Total Theoretical Shear Capacity (V_u):

V_u = 8.722 + 4.714 = 13.436\text{ kN}

4. Practically Observed Shear Resistance (V_exp):

V_{exp} = \frac{P}{2} = \frac{105.4}{2} = 52.7\text{ kN}

6. Results Summary

The final outcomes summarize the structural capabilities observed during the testing of the Beam in Pure Shear.

28 Days Compressive Strength

25.98 MPa

Initial Crack Load

35.6 kN

Theoretical Shear Capacity (V_u)

13.436 kN

Experimental Shear Resistance

52.7 kN

7. Discussion and Conclusion

The experimental shear resistance of 52.7 kN was significantly higher than the theoretical shear capacity of 13.436 kN as calculated using the code IS 456:2000.

Initially, fine vertical cracks appeared near the mid-span of the beam. As the applied load increased, inclined diagonal cracks developed near the support region and propagated towards the loading point. The beam ultimately failed by diagonal tension shear failure. A crack width of 4 mm was successfully observed prior to the ultimate failure point.