6.12 A uniform beam 4 m long is simply supported at its ends, where couples are applied, each 3 kN m in magnitude but opposite in sense. If E = 210 GN/m² and I = 90 × 10-6 m² determine the magnitude of the deflection at mid-span. What load must be applied at mid-span to reduce the deflection by half? [0.317 mm, 2.25 kN]

A 2.0 m wide strip foundation is placed in sand at 1.0 m depth. The properties of the sand are: = 19.5 kN/m3, c = 0 and =34. Determine the maximum wall load that the foundation can carry, with a factor of safety of 3.0, using a. Terzaghis original bearing capacity equation with his bearing capacity factors b. Meyerhofs modified bearing capacity equation with appropriate factors (Tables 16.2 and 16.3).

A column in a building is subjected to the following load effects: 9 kips compression from dead load 5 kips compression from roof live load 6 kips compression from snow 7 kips compression from 3 inches of rain accumulated on the roof 8 kips compression from wind a. If lead and resistance factor design is used, determine the factored load (required strength) to be used in the design of the column. Which AISC load combination controls? b. What is the required design strength of the Column? c. What is the required nominal strength of the column for a resistance factor of 0.90? d. If allowable strength design is used, determine the required load capacity (required strength) to be used in the design of the column. Which AISC load combination controls? e. What is the required nominal strength of the column for a safety factor of 1.67?

A beam is part of the framing system for the floor of an office building. The floor is subjected to both dead loads and live loads. The maximum moment caused by the service dead load is 45 ft-kips, and the maximum moment for the service live load is 63 ft-kips (these moments occur at the same location on the beam and can therefore be combined). a. If load and resistance factor design is used, determine the maximum factored bending moment (required moment strength). What is the controlling AISC load combination? b. What is the required nominal moment strength for a resistance factor of 0.90? c. If allowable strength design is used, determine the required moment strength. What is the controlling AISC lead combination? d. What is the required nominal moment strength for a safety factor of 1.67?

A W1422 acts compositely with a 4-inch-thick floor slab whose effective width b is 90 inches. The beams are spaced at 7 feet 6 inches, and the span length is 30 feet. The superimposed loads are as follows: construction load = 20 psf, partition load = 10 psf, weight of ceiling and light fixtures = 5 psf, and live load = 60 psf, A992 steel is used, and fc=4 ksi. Determine whether the flexural strength is adequate. a. Use LRFD. b. Use ASD.

A tall cylindrical silo carrying flour is to be supported by a 1.5 m wide ring beam that can be designed as a continuous foundation. The inner and outer diameters of the ring are 10 m and 13 m, respectively. The soil at the site is entirely sand (ф′ = 35°, γ = 19 kN/m3) and the ring beam is placed on the ground with Df = 0. Determine the maximum silo load that can be carried by the ring beam, assuming that the entire load is transferred to the ground through the ring beam.

Refer to Figure 10.43. A strip load of q = 1450 lb/ft2 is applied over a width with B = 48 ft. Determine the increase in vertical stress at point A located z = 21 ft below the surface. Given x = 28.8 ft. Figure 10.43