The timber member of Example 1 is used as a simply supported beam on a 16-ft span carrying a uniformly distributed line load of 400 lb/ft as shown below. Calculate the maximum induced bending stress. Neglect the weight of the beam. 400 lb/ft 16' h = 11.5" b = 7.5" X- X Centroidal axis and neutral axis 0 Example 1 - Bending Stress 2 ksi N 6 in. 2 ksi 6 in. 6 in. A

Compute the maximum bending moment, maxi- mum deflection and the maximum bending stress for a railroad rail subjected to a single wheel load of 100 kN. The foundation modulus k = 15 MN / m². Assume that I = 400 × 10-8 m², E = 200 GN/m², the depth of the rail is 180 mm and that the distance of the centroidal axis of the cross-section of the rail from the top surface is 100 mm.

The Simply supported beam in Figure has a rectangular cross section 120 mm wide and 200 mm high. (1)Compute the reaction forces Ra and Point RE. (2)Compute the maximum bending stress in the beam. - --- AAIL (4)Compute the bending stress at a point on section B that is 25 mm below the top of the beam. |15 kN 6 kN/m 100 mm NA - В ID 100 mm 0.8 m 120 mm 2 m 1.0 m RA RE (a)

Consider an 8-m long simply supported T-beam with overhangs loaded as shown below. 200 mm w kN/m 50 mm 50 kN-m 50 kN-m 200 mm 2 m 4 m 2 m 50 mm 1. Determine the location of the neutral axis measured from the top of the beam and the moment of inertia (in mm4) of the section about its neutral axis. Draw the shear and bending moment diagrams. Annotate all relevant values and distances. Determine the magnitude of the maximum negative 2. moment. Determine the minimum allowable strength of the beam in tension and the minimum allowable strength of the beam in compression. 3. Determine the maximum allowable load, w (in kN/m), that can be applied pn the beam. 4. B.

3. For the structure carrying a uniform load of 4 kN/ m, compute the internal axial force, shear force, and Answer: Vc = 2 kN, Mc = 4 kNm, Nc = 24 kN bending moment at point C in the beam. 4 kN/ m |C B 3 m 2 m -2 m 2 m

The simply supported beam with following cross section is loaded with concentrated loads and uniform load as shown. Determine a) the maximum tensile and compressive bending stress if P= 150 kip and w = 10 kip/ft, and b) the allowable uniform load w if the allowable bending stress is 24 Ksi and P = 15w. 3.169 in and c 1.5 inch Draw the FBD and calculate the reaction forces and shear and bending moment diagram. Draw the stress profile. Determine the maximum bending moment and its location 0.25 in. 3 ft 3 ft -0.25 in. 3 in. 10 ft 0.25 in. 3 in. -

A square footing 2.4 m x 0.34 m thick supports a 300 mm square column at its center. Column loads are service conditions: DL = 380 kN LL = 229 kN f’c = 21 MPa fy = 415 MPa Concrete cover to the centroid of steel reinforcement = 100 mm   Calculate the maximum ultimate bending moment in the slab.  Write your final answer as whole number with the unit of kN-m.

1. 2. 10 mm 10 mm 3. 5 mm 100 mm A beam section as shown in the sketch is subjected to a bendingmoment of Mx = 4 kN.m and a shear force of V = 2.5KN. 50 mm 100 mm Calculate the position of the centroid and the the second moment of area of the section about the sentroid horizontally. Draw the bending stress distribution through the height of the beam by calculating the bending stress at the critical positions Draw the shear stress distribution trough the height of the beam by calculating the shear stress below the flanges and at the centroid. 4. Draw the stress condition below the flanges, at the centroid and at the top and bottom of the beam.(7) 5. Draw the shearflow through the section. Show calculations

The horizontal beam ABC of an oil-wellpump has the cross section shown in the figure. If thevertical pumping force acting at end C is 9 kips andif the distance from the line of action of that force topoint B is 16 ft, what is the maximum bending stressin the beam due to the pumping force?

An A-36 steel beam of following cross section is part of a bridge and it is subjected loading as shown. mmmmm 35 ft 250 lb/ft 10 in 35 ft 50 ft 25 in 600 lb/ft * Assume that the bridge has a self-weight of 250 lb/ft and due to the truck, the loading is now 600 lb/ft for the 50 feet section as shown in the picture above. Now if the maximum bending moment due to the truck is 865.625 kip-ft, that translates to a maximum bending stress as shown in the table below. 25 in 50 ft 35 ft Maximum Bending stress (kpsi) Cross-sectional shape Yield strength of steel Moment of inertia of beam A-36 9.97 kpsi Rectangular I-shaped Beam 36 kpsi 36 kpsi 21.633 kpsi The cross-sectional dimensions of both shapes are shown below. 250 lb/ft 10 in 35 ft (in) 13020 6290 Consider yourself as an engineer assigned to this bridge construction and discuss the suitable options for the optimal cross-section of the bridge. Note that from the data shown in the table, both rectangular and I-beam cross-sections have…