Dead loads are gravity loads of constant magnitudes and fixed positions that act permanently on the structure. Such loads consist of the weights of the structural system itself and of all other material and equipment permanently attached to the structural system. For example, the dead loads for a building structure include the weights of frames, framing and bracing systems, floors, roofs, ceilings, walls, stairways, heating and airconditioning systems, plumbing, electrical systems, and so forth. The weight of the structure is not known in advance of design and is usually assumed based on past experience. After the structure has been analyzed and the member sizes determined, the actual weight is computed by using the member sizes and the unit weights of materials. The actual weight is then compared to the assumed weight, and the design is revised if necessary. The unit weights of some common construction materials are given in Table 2.1. The weights of permanent service equipment, such as heating and air-conditioning systems, are usually obtained from the manufacturer.

# Example 2.1

The floor system of a building consists of a 5-in.-thick reinforced concrete slab resting on four steel floor beams, which in turn are supported by two steel girders, as shown in Fig. 2.1(a). The cross-sectional areas of the floor beams and the girders are 14.7 in.2 and 52.3 in.2, respectively. Determine the dead loads acting on the beams CG and DH and the girder AD.

**Solution **

Beam CG As shown in Fig. 2.1(a), the portion of the slab supported by beam CG has a width of 10 ft (i.e., half the distance between beams CG and BF plus half the distance between beams CG and DH) and a length of 24 ft. This surface area (24 10 ¼ 240 ft2) supported by beam CG (the shaded rectangular area in Fig. 2.1(a)) is referred to as the tributary area for beam CG. We use the unit weights of reinforced concrete and structural steel from Table 2.1 to compute the dead load per foot of length of beam CG as follows:

This load is uniformly distributed on the beam, as shown in Fig. 2.1(b). This figure also shows the eactions exerted by the supporting girders at the ends of the beam. As the beam is symmetrically loaded, the magnitudes of the reactions are equal to half of the total load acting on the beam:

Note that the magnitudes of these end reactions represent the downward loads being transmitted to the supporting girders AD and EH at points C and G, respectively.

Beam DH The tributary area for beam DH is 5 ft wide and 24 ft long. The dead load per foot of length of this beam is computed as follows:

Girder AD Because of the symmetry of the framing system and loading, the loads acting on beams BF and AE are the same as those on beams CG and DH, respectively. The load on girder AD consists of the uniformly distributed load due to its own weight, which has a magnitude of

and the concentrated loads transmitted to it by the beams at points A, B, C, and D, as shown in Fig. 2.1(d).