A simply supported composite beam 2 m long carries a uniformly distributed load of intensity q = 2.3 kN/m (see figure). q=2.3 kN/m 2 m s (a) Find the maximum bending stresses (Enter the magnitudes.) 0 100 mm The beam is constructed of a wood member, 100 mm wide by 150 mm deep, and is reinforced on its lower side by a steel plate 8 mm thick and 100 mm wide. (Assume that the component parts of the beam are securely bonded by adhesives or connected by fasteners. Also, be sure to use the general theory for composite beams described in the section titled 'Composite Beams.") and a, (in MPa) in the wood and steel, respectively, due to the uniform load if the moduli of elasticity are E = 10 GPa for the wood and E₂ = 210 GPa for the steel. 1.7377777777 ✓ MPa 12.8119 ✓ MPa 150 mm 8 mm (b) Find the required thickness (in mm) of the steel plate so that the steel plate and wood reach their allowable stress values, as = 100 MPa and aw = 8.3 MPa, simultaneously under the maximum moment. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. mm

A simply supported wood beam of rectangular cross section and span length 1.2 m carries a concentrated load P at midspan in addition to its own weight (see figure). The cross section has width 140 mm and height 240 mm. The weight density of the wood is 5,4 kN/m3Calculate the maximum permissible value of the load P if (a) the allowable bending stress is MPa and (b) the allowable shear stress is 0,8 MPa

5.10-8 A bridge girder AB on a simple span of length L = 14 m supports a distributed load of max- imum intensity q at mid-span and minimum intensity 412 at supports A and B that includes the weight of the girder (see figure). The girder is constructed of three plates welded to form the cross section shown. Determine the maximum permissible load q based upon (a) an allowable bending stress oallow = 110 MPa and (b) an allowable shear stress 7 low = 50 MPa. 450 mm 32 mm B L= 14 m - 16 mm- 1800 mm 32 mm 450 mm

A simply supported wood beam of length L = 11 ft carries a concentrated load P at midspan, as shown. The cross-sectional dimensions of the beam are b = 7 in. and h = 13 in. If the allowable shear strength of the wood is 125 psi, determine the maximum load P that may be applied at midspan. Neglect the effects of the beam's self-weight. A Answer: P = 2 P B lb 12 L C X Z b h

2) 5.5-5 A rectangular beam ABC (L = 15 ft; h= 12 in.) has simple supports at A and B and an overhang from B to C. A uniform load with intensity q = 150 lb/ft is applied to the beam and the section modulus S = 50 in³. Determine the maximum stress max in the beam. (Clue: Check for local maximum and minimum in bending moment diagram. The maximum magnitude will produce maximum stress). PROBLEM 5.5-5 MH17 B 10 ft 5 ft

H.W 4 A simple beam on a 10 ft span supports a uniform load of intensity 800 lb/ft (see figure). The beam consists of a wood member (4 in. X 11.5 in. in cross section) that is reinforced by 0.25 in. thick steel plates on top and bottom. The moduli of elasticity for the steel and wood are E, 30 × 10° psi and E, = 1.5 × 10° psi, respectively. Calculate the maximum bending stresses o, in the steel plates and o,, in the wood member due to the uniform load. y 0.25 in. 800 lb/ft 11.5 in. 0.25 in. 10 ft 4 in. FIGURE 4

5.8-6) A cantilever beam of length L = 2 m sup- ports a load P = 8.0 kN (see figure). The beam is made of wood with cross-sectional dimensions 120 mm X 200 mm. Calculate the shear stresses due to the load P at points located 25 mm, 50 mm, 75 mm, and 100 mm from the top surface of the beam. From these results, plot a graph showing the distribution of shear stresses from top to bottom of the beam. P = 8.0 kN 200 mm L = 2 m 120 mm PROBLEM 5.8-6

A cantilever beam of rectangular cross section is subjected to a concentrated load P = 150 kN acting at the free end (see Figure 1). The beam has width b = 80 mm. and height h = 260 mm. Point A is located at distance c = 0.5 m from the free end and distance d = 220 mm. from the bottom of the beam. a) Using Mohr's circle, calculate the principal stresses oi and o2 and the maximum shear stress Tmax at point A. b) Show these stresses on sketches of properly oriented elements. A•

Q3) A circular bar of 25mm diameter is formed into a semicircular arch and loaded as shown in the figure. Determine the maximum bending stress. Assume that the flexure formula for straight beams is applicable. 200KN 100KN R=1.5m 230°

A beam is loaded as shown in the figure. The length 1-20 in. and the load locations are a=10 in. and b= 15 in. The beam is steel with E = 30 Mpsi. The magnitude of the concentrated force is F= 500 lb and the distributed load is 50 lb/in. The dimensions of the beam cross-section are h = 5 and t = 2. You will be finding the deflection and slope at the end of the beam. a b 1 W F