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Sample Problems Problem 16.1 The moment of inertia about the neutral axis for the T-beam shown is most nearly (A) 36 in 4 (C) 236 in 4 (B) 136 in 4 (D) 736 in 4 This procedure covers the determination of the moment of inertia about the neutral axis. Step 1. Calculate the location of neutral axis from the base of the beam. Use Equation No. 191 (Y), page 318. Press ENTER. A? 0 R/S Thickness of the lower flange (in) B? 0 R/S Width of the lower flange (in) H? 6 R/S Height of the web (in) G? 6 R/S Width of the upper flange (in) F? 2 R/S Thickness of the upper flange (in) Y = 5.0000 -- Location of neutral axis from the bottom of the beam (in) Step 2. Calculate the moment of inertia. Use Equation No. 191 (I), page 318. Press ENTER. Press R/S every time you are prompted. You ll get I = 136.0000 (in 4 ). The answer is (B). Notes: For inverted T-beam, G and F are zero. For T-beam, A and B are zero. 328
Problem 16.2 The moment of inertia about the neutral axis for the symmetrical I-beam shown is most nearly (A) 533 in 4 (C) 783 in 4 (B) 693 in 4 (D) 2,133 in 4 Calculate the moment of inertia about the neutral axis. Use Equation No. 192, page 320. Press ENTER. B? 6 R/S Width of lower and upper flanges (in) A? 2 R/S Thickness of lower and upper flanges (in) H? 8 R/S Height of the web (in) I = 693.3333 -- Moment of inertia about the neutral axis (in 4 ) The answer is (B). 329
Problem 16.3 A 10-ft-long, simply supported T-beam is carrying a uniform load of 4 kips/ft. The maximum tensile bending stress and maximum compressive bending stress are most nearly Maximum Tensile Bending Stress (ksi) Maximum Compressive Bending Stress (ksi) (A) 19 10 (B) 29 17 (C) 32 18 (D) 35 22 This practice can be used to determine the maximum tensile bending stress and maximum compressive bending stress of T-beam with uniform load. Step 1. Calculate the maximum moment for simply supported beam with uniform distributed load. Use Equation No. 186, page 314. Press ENTER. W? 4 R/S Uniform distributed load on the beam (kips/ft) L? 10 R/S Length of the beam (ft) M = 50.0000 -- Maximum moment (ft-kips) Step 2. Compute the location of neutral axis from the base of the beam. Use Equation No. 191 (Y), page 318. Press ENTER. A? 0 R/S Thickness of the lower flange (in) B? 0 R/S Width of the lower flange (in) H? 5 R/S Height of the web (in) G? 6 R/S Width of the upper flange (in) F? 2 R/S Thickness of the upper flange (in) 330
Y = 4.4091 -- Location of neutral axis from bottom of the beam (in) Step 3. Determine the moment of inertia. Use Equation No. 191 (I), page 318. Press ENTER. Press R/S every time you are prompted. You ll get I = 91.6515 (in 4 ). Step 4. Calculate the maximum tensile bending stress for simply supported beam. Use Equation No. 193, page 321. Press ENTER. Press R/S every time you are prompted. You ll get S = 28.8643 (ksi). Step 5. Calculate the maximum compressive bending stress for simply supported beam. Use Equation No. 194, page 322. Press ENTER. Press R/S every time you are prompted. You ll get S = 16.9615 (ksi). The answer is (B). Problem 16.4 A simply supported beam is carrying 10 kips load in the middle. The modulus of elasticity of the beam is 29,000 ksi. The maximum deflection in the beam is most nearly (A) 0.1 in (B) 0.2 in (C) 0.3 in (D) 1 in This procedure is intended to be used in calculating the maximum deflection in the beam. Step 1. Calculate the location of neutral axis from the base of the beam. Use Equation No. 191 (Y), page 318. Press ENTER. A? 0 R/S Thickness of the lower flange (in) B? 0 R/S Width of the lower flange (in) H? 5 R/S Height of the web (in) G? 6 R/S Width of the upper flange (in) 331
F? 2 R/S Thickness of the upper flange (in) Y = 4.4091 -- Location of neutral axis from the base (in) Step 2. Calculate the moment of inertia of the beam. Use Equation No. 191 (I), page 318. Press ENTER. Press R/S every time you are prompted. You ll get I = 91.6515 (in 4 ). Step 3. Calculate the deflection of simply supported beam with load in the middle. Use Equation No. 197, page 324. Press ENTER. P? 10 R/S Load on the beam (kips) L? 10 R/S Length of the beam (ft) E? 29000 R/S Modulus of elasticity of the beam (ksi) I? 91.6515 R/S Moment of inertia of the beam (in 4 ) D = 0.1354 -- Maximum deflection of the beam (in) The answer is (A). 332