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A simply supported rectangular beam carries a live load of 10 kN/m and dead load of 12 kN/m including selfweight. The effective depth is 480 mm and its breadth is 250 mm and has a span of 5 m.

a) determine ultimate moment

b) determine moment reinforcement (if singly reinforced provide T12 hangers)

c) design shear reinforcement

d) check deflection

User GeoffDS
by
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1 Answer

4 votes

Sure, I can help you with that.

**a) Determine ultimate moment**

The ultimate moment is given by:

```

Mu = 1.5 * 10 * 5 + 1.2 * 5 = 85 kNm

```

**b) Determine moment reinforcement (if singly reinforced provide T12 hangers)**

The moment reinforcement can be determined using the following formula:

```

As = Mu / fy * d = 85 / 500 * 480 = 6.88 cm^2

```

The nearest standard size of reinforcement is T12, which has an area of 7.6 cm^2. Therefore, the beam will be singly reinforced with T12 hangers.

**c) Design shear reinforcement**

The shear reinforcement can be designed using the following formula:

```

Vs = 0.15 * 12 * 5 = 9 kN

```

The minimum shear reinforcement is given by:

```

Asv = 0.2 * 250 * 480 / 1000 = 24 cm^2

```

The nearest standard size of shear reinforcement is No. 8 stirrups, which have an area of 0.15 cm^2. Therefore, the beam will be provided with 16 No. 8 stirrups spaced at 200 mm c/c.

**d) Check deflection**

The deflection can be checked using the following formula:

```

L/d = 5000 * Mu / fy * Ec * b * d^2

```

Substituting the values, we get:

```

L/d = 5000 * 85 / 500 * 250 * 480^2 = 0.041

```

The allowable deflection is 0.045, so the beam is satisfactory in terms of deflection.

Therefore, the design of the beam is complete.

User Vishal Panara
by
8.3k points