EAS 453 Pre-stressed Concrete Design Stress Limit of Pre-stressed Concrete 1Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM

Basic Principles Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 2

Basic Principles Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 3

Basic Principles Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 4

Example 1 : Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 5 A pre-stressed concrete rectangular beam 500 mm x 750 mm with 7.30m span is loaded by a uniform load of 45 kN/m including its own self-weight. The pre-stressing tendon is located 145 mm below the neutral axis at mid-span of the section (take it as +ve sign) and produces an effective pre-stress of 1620 kN. Calculate the fibre stresses in the concrete at mid-span. Assume compressive stress as +ve. Answer, P = 1620 kN A= 500 x 750 = 375,000 mm 2 e= 145 mmI= bd 3 /12 = 500x750 3 /12 = x mm 4 y= 750/2 = 375 mm (top and bottom) Moment at mid-span = 45 x /8= kNm f = P/A ± Pey/I ± M x y/I (y/I = 1/Z) (prestress) (eccentric) (load)

Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 6 for top fibre, = 1620 x 1000 – 1620 x 1000 x 145 x x 10 6 x , x x = 5.70 N/mm 2 (MPa) - compression for bottom fibre, = 1620 x x 1000 x 145 x x 10 6 x , x x = 2.94 N/mm 2 – compression

Example 2 : Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 7 Compute the mid-span stresses for the pre-stress beam with parabolic tendon as shown in figure below. Top fibre? Bottom fibre? 45kN/m e=145mm Prestress 1620kN

Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 8 At Transfer This is when the concrete first feels the pre-stress. The concrete is less strong but the situation is temporary and the stresses are only due to pre-stress and self weight. At Service The stresses induced by the SLS loading, in addition to the pre-stress and self weight, must be checked. At service stage, the concrete has its full strength but losses will have occurred and so the pre-stress force is reduced.

STRESS LIMIT Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 9 a.Concrete  Minimum concrete grade for PC is strongly recommended at 35 N/mm 2 for pre-tension and 40 N/mm 2 for post- tension (Clause )  Concrete strength versus age is given under Table 7.1  Important information for concrete is given under Section 7 BS 8110

Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 10

b.Strand Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 11 TypeNominal Diameter (mm) Characteristic Strength, f pu (N/mm 2 ) Cross sectional, A ps Area (mm 2 ) Breaking Load, A ps f cu (kN) 7-wire (standard) wire (super) wire

c.Classification – serviceability & transfer Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 12  i. Limit of tensile stress at service  Clause of BS 8110 as recommended by CEB-FIP (Comite Europeen Du Beton – Federation Internationale de la Precontrainte). The basis are :-  Class 1 – No tensile stress  Class 2 – flexural tensile stresses but no visible cracking  Class 3 – flexural tensile stresses but surface width of cracks not exceeding 0.1 mm (severe environments) nor 0.2 mm (others)

Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 13  Flexural tensile stress limit due under service load under Clause  Class 1 – No tensile stress  Class 2 – Design tensile stress should not exceed the design flexural tensile strength for pre-tensioned members nor 0.8 of the design flexural tensile strength for post-tensioned members. Limiting tensile stresses are 0.45√f cu for pre-tension members and 0.36√f cu for post-tensioned members  In general, the design of Class 1 and Class 2 members is controlled by the concrete tension limitations Design flexural tensile stresses for Class 2 members (N/mm 2 ) – T4.1 Type ofDesign stress for Pre-stressedconcrete grade Member Pre-tensioned Post-tensioned

Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 14  Class 3 – cracking is allowed but assumed the concrete section is uncracked and that design hypothetical tensile stresses exist at the limiting crack width as in Clause  The cracking in pre-stressed concrete flexural members is dependent on the member depth and the design stress given in Table 4.2 BS 8110 should be modified by multiplying the appropriate factor from Table 4.3 Design hypothetical flexural tensile stresses for Class 3 members (N/mm 2 ) – Table 4.2 LimitingDesign stress for concrete grade GroupCrack Width (mm) 30 (N/mm 2 ) 40 (N/mm 2 ) 50 and over (N/mm 2 ) Pre-tensioned tendons Grouted post tensioned tendons Pre-tensioned tendons……

Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 15  ii.Limit of design tensile stresses in flexure at transfer for beams  Clause of BS 8110  Class 1 – 1.0 N/mm 2  Class 2 – 0.45√f ci for pre-tensioned members and 0.36√f ci for post-tensioned members. f ci = concrete strength at transfer  Class 3 – should not exceed the limit for Class 2 in. If the stress exceeded, members should be designed as cracked  iii.Limit of compressive stress at service  Clause  In flexural members, the compressive stress should not exceed 0.33f cu at the extreme fibre (for all classes) except for continuous beam or other statically indeterminate structures, this value can be increased to 0.4f cu

Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 16  iv.Limit of compressive stress at transfer  Clause  In flexural members, the compressive stress should not exceed 0.5f ci at the extreme fibre (for all classes) nor 0.4f ci for near uniform distribution of pre- stress  Notes ** 1. The guidelines on the selection to use Class 1,2 or 3 members are not explained in details in BS In general, Class 1 is used for structures that are not ‘allowed’ to cracks such as water retaining structures, structures subjected to aggressive environment (maritime) or abnormal/high/cyclic loadings (bridges & highways) 3. Class 2 & 3 use lesser amount of pre-stressing tendons – cheaper 4. Class 1 – more likely to have cambering due to excessive upward deflection and the design load are over estimate. 5. The design principles for Class 1 and 2 are almost the same

Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM Class 3 – often known as partial pre-stressing, represents a form of construction which is intermediate between reinforced and pre-stressed concrete. 7. The limits shown above also serve to avoid excessive deflection (however, deflection must be checked) 8. the constant for limiting the compressive stress (0.5) at transfer is higher compared to at service (0.33). This is due to the fact that pre-stressing force at transfer decrease with time due to pre-stress loss at simultaneously the concrete is in the process of gaining its full strength

Example 1 Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 18  A simply supported Class 1 post-tensioned beam will be stressed at concrete strength of 30 N/mm 2. Determine all the stresses limit at transfer and at service if the concrete strength at service is 40 N/mm 2.  Limit of tensile stress at transfer = -1.0 N/mm 2  Limit of tensile stress at service= 0  Limit of compressive stress at transfer= 15 N/mm 2  Limit of compressive stress at service= 13.2 N/mm 2

Example 2 Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 19  A simply supported Class 2 post-tensioned beam will be stressed at concrete strength of 30 N/mm 2. Determine all the stresses limit at transfer and at service if the concrete strength at service is 40 N/mm 2.  Limit of tensile stress at transfer = N/mm 2  Limit of tensile stress at service= -2.3 N/mm 2  Limit of compressive stress at transfer= 15 N/mm 2  Limit of compressive stress at service= 13.2 N/mm 2

d.Notations and sign conventions Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 20  varies (US – UK)  F. K. Kong suggested the followings to be compatible with UK practice i. Moment due to applied load Sagging = positive Hogging= negative ii. Stress Compression= positive Tension= negative iii. Eccentricity of cable force Downward (from N.A)= positive Upward (from N.A.)= negative

Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 21

Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 22 f t ’= top fiber stress at transfer condition f b ’= bottom fiber stress at transfer condition f t = top fiber stress at service condition f b = bottom fiber stress at service condition f’ min = permissible tensile stress at transfer condition f’ max = permissible compressive stress at transfer condition f min = permissible tensile stress at service condition f max = permissible compressive stress at service condition P o = pre-stressing force at transfer P e = pre-stressing force at service (effective pre-stressing) K= loss factor M min = moment at transfer M max = moment at service Zt= section modulus for top of section Zb= section modulus for bottom of section e= tendon eccentricity

e.Basic Equations Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 23  The design of pre-stressing requirements is based on the manipulation of the 4 basic equations (as shown below) describing the stress distribution across the concrete section.  These are used in conjunction with the permissible stresses appropriate to the class of member coupled with the final pre-stress force after losses and the maximum and minimum loadings on member  These loadings must encompass the full range that the member will encounter during its life  Partial factor of safety = 1.0 (SLS) both dead & live load

Positive tendon (tendon placed below the Neutral Axis) Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 24

Negative tendon (tendon placed above the Neutral Axis) Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 25

Dr. NORAZURA MUHAMAD BUNNORI (PhD), USM 26  Note :  all stresses (at transfer or service) shall not exceed the limit (tensile or compressive) regardless whether at top or bottom  The above equations is meant at any section considered (mid-span, end span, quarter span, etc)  K (pre-stress loss factor) must be assumed first at this stage. A value of 0.8 or 0.75 is considered appropriate