Reinforced Concrete Beam Design (NZS 3101-95) Calculations

11 Nov 2011 11:12:36 REINFORCED CONCRETE BEAM DESIGN (NZS 3101-95) Material Properties Concrete strength, 30 MPa f_c Concrete stress block factors, α_1 if 0.85 0.004 f_c MPa 55 0.75 0.75 else if 0.85 0.004 f_c MPa 55 f_c MPa 55 0.85 0.85 else 0.85 0.004 β_1 if 0.85 0.008 f_c MPa 30 --> α_1 0.85 --> β_1 0.85 0.65 0.65 else if 0.85 0.008 f_c MPa 30 f_c MPa 30 0.85 0.85 else 0.85 0.008 Steel bars yield strength, f_y 400 MPa f_ys 240 MPa Modulus of elasticity of steel reinforcement, E_s 200000 MPa Beam Dimensions Width, b_w 400 mm Depth, h 400 mm Concrete cover, c_v 30 mm Main bars diameter, D_b 22 mm 1/4 11 Nov 2011 11:12:36 Strirrup bars diameter, 10 mm d_b Effective depth, Tension steel (assumed as one layer), d h c_v d_b D_b 2 --> d 349 mm adjust and overwrites for steel bars if more than one layer, 300 mm d Compression steel, d_p c_v d_b D_b 2 --> d_p 51 mm adjust and overwrites for steel bars if more than one layer, 51 mm d_p D e s i g n f o r F l e x u r e Factored negative or positive moment, 300 kN m M_u Strength reduction factors for bending, φ_b 0.85 Depth of the compression block, a d d 2 2 M_u α_1 f_c φ_b b_w --> a 155.792 mm Neutral axes depth at balanced conditions, c_b 600 MPa d 600 MPa f_y --> c_b 180 mm Maximum allowed depth of the compression block, a_max 114.75 mm a_max 0.75 β_1 c_b b_type if a a_max "CASE 1 - Singly Reinfoced Beams" else "CASE 2 - Doubly Reinforced Beams" --> --> b_type "CASE 2 - Doubly Reinforced Beams" CASE 1 a a_max 0 “(1) TRUE” area of tensile steel reinforcement, M_u A_s φ_b f_y d a 2 --> 2 A_s 3972.705 mm N_b 10.451 bars Number of bars required, N_b A_s 1 2 π D_b 4 --> CASE 2 a a_max 1 “(1) TRUE” compression reinforcement is required, 2/4 11 Nov 2011 11:12:36 Compressive force developed in the concrete alone, C α_1 f_c b_w a_max --> 1170.45 kN C Moment resisted by the concrete and bottom steel, M_c C d a_max φ_b 2 --> M_c 241.383 kN m Moment resisted by compression steel and tensile steel, M_s M_u M_c --> M_s 58.617 kN m Compression steel required, c a β_1 --> c c 183.285 mm d_p c f_sp1 0.003 E_s f_sp min A_sp M_s f_sp α_1 f_c d f_y f_sp1 --> f_sp1 433.047 MPa --> f_sp 400 MPa d_p φ_b --> A_sp 739.521 mm Number of bars required, A_sp 1 2 π D_b 4 N_b --> N_b 1.945 bars Required tensile steel for balancing the compression in concrete, M_c a_max φ_b 2 A_s1 f_y d --> A_s1 2926.125 mm 2 Tensile steel for balancing the compression in steel, A_s2 A_s f_y d M_s d_p φ_b --> A_s1 A_s2 --> A_s2 692.377 mm 2 3618.502 mm 2 A_s Number of bars required, N_b A_s 1 2 π D_b 4 --> N_b 9.519 bars Minimum and maximum tensile reinforcement, A_smin f_c MPa b_w d 4 f_y 4 A_s 3 0.004 b_w d max --> A_smin 4824.669 mm Beam flexural tensile steel is limited to a maximum, A_smax min 0.025 b_w d f_c 10 MPa b_w d 6 f_y D e s i g n f o r --> A_smax 2000 mm S h e a r Shear force, V 200 kN Strength reduction factor for shear, φ_s 0.65 Shear capacity provided by the concrete, 3/4 2 2 2 11 Nov 2011 11:12:36 v_b A_s 0.07 10 b_w d v_c v_b --> f_c MPa v_c --> v_b f_c MPa 0 2.035 MPa 2.035 MPa Checked, 70 MPa 1 f_c MPa v_b f_c Checked, 0.08 v_b 0.2 Average shear stress is computed for a rectangular beam, V b_w d v --> v 1.667 MPa Average shear stress is limited to a maximum, v_max 1.1 f_c MPa 0.2 f_c 9.0 MPa min v_max 6 MPa --> Checked, v v_max 1 Shear reinforcement per unit length, A_v v_c 2 2 mm if v φ_s 0.00 mm else v_c v v φ_s v_c 2 0.35 MPa b_w mm f_ys else v φ_s v_c b_w mm φ_s f_ys if φ_s s 0.35 MPa --> 1.0 mm A_v s 0.882 mm 2 mm Stirrups legs, n_s 2 legs A_sv n_s 1 2 π d_b 4 --> A_sv 157.08 mm 2 Stirrups spacing required, S_sp A_sv s A_v --> S_sp 178.134 mm 4/4 A_v 0.882 mm 2

Reinforced Concrete Beam Design (NZS 3101-95) Calculations

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