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Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931

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Section
BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 2, Problem 7P
Textbook Problem
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The floor system of a gymnasium consists of a 130 mm thick concrete slab resting on four steel beams (A = 9,100 mm2) that, in turn, are supported by two steel girders (A = 25,600 mm2), as shown in Fig. P2.7. Determine the dead loads acting on beam BF and girder AD.

FIG. P2.7, P2.10

Chapter 2, Problem 7P, The floor system of a gymnasium consists of a 130 mm thick concrete slab resting on four steel beams

To determine

Find the dead load acting on the beam BF and girder AD.

Explanation of Solution

Given information:

Consider the floor system of gymnasium.

The thickness of the concrete slab is 130mm.

The area of the steel beams is Asb=9,100mm2.

The area of the steel girder is Asg=25,600mm2.

Calculation:

Show the slab as shown in Figure 1.

Refer to Figure 1.

Refer Table 2.1, “Unit Weight of the Construction Materials” in the textbook.

The unit of the structural steel is γs=77kN/m3.

The unit of the reinforced concrete is γc=23.6kN/m3.

Show the tributary area of the beam BF as shown in Figure 2.

Refer Figure 1 and Figure 2.

Calculate the dead load of concrete slab acting on  the beam per unit length of the beam as follows:

Dead of concrete slab=γc×(UnitLengthoftheTributaryArea×WidthoftheTributaryArea×Thicknessoftheconcreteslab)=23.6kN/m3×(1m×5m×130mm×1m1000mm)=23.6×(1×5×0.13)15.34kN

Calculate the dead load of steel beam acting per unit length of the beam as follows:

Dead of steel beam=γs×(UnitLengthoftheTributaryArea×Area of the steel beam)=77kN/m3×(1m×9100mm2×(1m1000mm)2)=77×(1×9100×106)0.7007kN

Calculate the total load acting on the steel beam per unit length of the beam as follows:

Total Dead load on the steel beam=(Dead load on the concrete slab+Dead load of the steel beam)=(15.34+0.7007)=16.04kN

The total dead load is distributed uniformly over the entire length of the beam

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